1 Pierre Descouvemont Université Libre de Bruxelles, Brussels, Belgium R-matrix theory of nuclear...
80
1 Pierre Descouvemont Université Libre de Bruxelles, Brussels, Belgium R-matrix theory of nuclear reactions 1. Introduction 2. General collision theory: elastic scattering 3. Phase-shift method 4. R-matrix theory ( theory) 5. Phenomenological R matrix ( experiment) 6. Conclusions
-
Upload
buck-payne -
Category
Documents
-
view
224 -
download
8
Transcript of 1 Pierre Descouvemont Université Libre de Bruxelles, Brussels, Belgium R-matrix theory of nuclear...
-
Pierre DescouvemontUniversit Libre de Bruxelles, Brussels, BelgiumR-matrix theory of nuclear reactionsIntroductionGeneral collision theory: elastic scatteringPhase-shift methodR-matrix theory ( theory)Phenomenological R matrix ( experiment)Conclusions
-
IntroductionGeneral context: two-body systems Low energies (E Coulomb barrier), few open channels (one) Low masses (A 15-20) Low level densities ( a few levels/MeV) Reactions with neutrons AND charged particlesErV=0>0Only a few partial waves contribute
-
Low-energy reactions Transmission (tunnelling) decreases with few partial waves semi-classic theories not valid astrophysics thermal neutrons
Wavelength =c/E (fm)~197/E(MeV) example: 1 MeV: ~200 fm radius~2-4 fm quantum effects importantSome references:C. Joachain: Quantum Collision Theory, North Holland 1987L. Rodberg, R. Thaler: Introduction to the quantum theory of scattering, Academic Press 1967J. Taylor : Scattering Theory: the quantum theory on nonrelativistic collisions, John Wiley 1972
-
Different types of reactions1. Elastic collision : entrance channel=exit channelA+B A+B: Q=0
2. Inelastic collision (Q0)A+B A*+B (A*=excited state) A+B A+B* A+B A*+B* etc..3. Transfer reactionsA+B C+D A+B C+D+E A+B C*+D etc 4. radiative capture reactions A+B C + gNOT covered herecovered here
-
2. Collision theory: elastic scattering
Assumptions: elastic scattering no internal structure no Coulomb spins zero Before collisionAfter collisionqCenter-of-mass system1212
-
Schrdinger equation: V(r)=interaction potential
Assumption: the potential is real and decreases faster than 1/rScattering wave functionsA large distances : V(r) 02 independent solutions :Incoming plane waveOutgoing spherical wavewhere: k=wave number: k2=2mE/2 A=amplitude (scattering wave function is not normalized) f(q) =scattering amplitude (length)
-
Cross sectionsqsolid angle dWCross sectionCross section obtained from the asymptotic part of the wave functionDirect problem: determine s from the potentialInverse problem : determine the potential V from sAngular distribution: E fixed, q variableExcitation function: q variable, E fixed,
-
How to solve the Schrdinger equation for E>0?
With (z along the beam axis)
Several methods: Formal theory: Lippman-Schwinger equation approximations Eikonal approximation Born approximation Phase shift method: well adapted to low energies Etc
-
Lippman-Schwinger equation:r is supposed to be large (r >> r') Y(r) must be known Y(r) only needed where V(r)0 approximations are possible Born approximation : Eikonal approximation: is solution of the Schrdinger equationWith =Green functionValid at high energies: V(r) E
-
3. Phase-shift methodDefinitions, cross sections Simple conditions: neutral systems spins 0 single-channelExtension to charged systemsExtension to multichannel problemsLow energy propertiesGeneral calculationOptical model
-
The wave function is expanded asWhen inserted in the Schrdinger equationTo be solved for any potential (real)For r V(r) =0=Bessel equation ul(r)= jl(kr), nl(kr)3.a Definition, cross section
-
For small xFor large xExamples: At large distances: ul(r) is a linear combination of jl(kr) and nl(kr):With dl = phase shift (information about the potential) If V=0 d=0Cross section:Provide the cross section
-
factorization of the dependences in E and q
General properties of the phase shiftsExpansion useful at low energies: small number of valuesThe phase shift (and all derivatives) are continuous functions of EThe phase shift is known within np: exp(2id)=exp(2i(d+np))Levinson theorem d(E=0) - d(E=)= Np , where N is the number of bound states Example: p+n, =0: d(E=0) - d(E=)= p (bound deuteron)
-
Interpretation of the phase shift from the wave functiondl0 V attractiveu(r)rV=0 u(r)sin(kr-lp/2) dl=0V0 u(r)sin(kr-lp/2+dl)
-
Resonances:=Breit-Wigner approximationER=resonance energy G=resonance width Narrow resonance: G small Broad resonance: G largeExample: 12C+pWith resonance: ER=0.42 MeV, G=32 keV lifetime: t=}/G~2x10-20 sWithout resonance: interaction range d~10 fm interaction time t=d/v ~1.1x10-21 s
-
3.b Generalization to the Coulomb potentialThe asymtotic behaviour Y(r) exp(ikz) + f(q)*exp(ikr)/r Becomes:Y(r) exp(ikz+h log(kr)) + f(q)*exp(ikr-h log(2kr))/r With h=Z1Z2e2/v =Sommerfeld parameter, v=velocityBessel equation:Coulomb equationSolutions: Fl(h,kr): regular, Gl(h,kr): irregularIngoing, outgoing functions: Il= Gl-iFl, Ol=Gl+iFl
-
Example: hard sphereV(r)raV(r)= for ra= Hard-Sphere phase shift
-
example : a+n phase shift l=0Special case: Neutrons, with l=0:F0(x)=sin(x), G0(x)=cos(x) d=-ka hard sphere is a good approximation
-
Elastic cross section with Coulomb:Still valid, but converges very slowly.Coulomb: exactNuclear= Coulomb cross section: diverges for q=0 increases at low energies
-
The total Coulomb cross section is not defined (diverges) Coulomb is dominant at small angles used to normalize data Increases at low energies Minimum at q=180o nuclear effect maximumfC(q): Coulomb part: exactfN(q): nuclear part: converges rapidly
-
One channel: phase shift d U=exp(2id)Multichannel: collision matrix Uij, (symmetric , unitary) with i,j=channelsGood quantum numbersJ=total spin p=total parityChannel i characterized by I=I1 I2 =channel spin J=I l l =angular momentumSelection rules: |I1- I2| I I1+ I2 | l - I| J l + I p=p1*p2* (-1) l Example of quantum numbersXXXXa+3He a=0+, 3He=1/2+p+7Be 7Be=3/2-, p=1/2+XXXXXXXX3.c Extension to multichannel problems
JI lsize1/2+1/20, 111/2-1/20, 113/2+1/21, 213/2-1/21, 21
JI lsize0+1 21 210-1 21 211+1 20, 1, 2 1, 2, 331-1 20, 1, 2 1, 2, 33
-
Cross sections Multichannel With:K1,K2=spin orientations in the entrance channelK1,K2=spin orientations in the exit channel
One channel:Collision matrix generalization of d: Uij=hijexp(2idij) determines the cross section
-
Then, for very low E (neutral system):One defines=logarithmic derivative at r=a (a large) 3.d Low-energy properties of the phase shiftsFor =0:Edl=0, a0l>0strong difference between l=0 and l>0Generalizationa=scattering length re=effective range
-
Cross section at low E:In general (neutrons): Thermal neutrons (T=300K, E=25 meV): only l=0 contributesexample : a+n phase shift l=0At low E: d~-ka with a>0 replusive
-
3.e General calculationwith: Numerical solution : discretization N points, with mesh size h ul(0)=0 ul(h)=1 (or any constant) ul(2h) is determined numerically from ul(0) and ul(h) (Numerov algorithm) ul(3h), ul(Nh) for large r: matching to the asymptotic behaviour phase shiftBound states: same ideaFor some potentials: analytic solution of the Schrdinger equationIn general: no analytic solution numerical approach
-
Example: a+a0+ E=0.09 MeV G=6 eV4+ E~11 MeV G~3.5 MeV2+ E~3 MeV G~1.5 MeVExperimental spectrum of 8BeExperimental phase shiftsPotential: VN(r)=-122.3*exp(-(r/2.13)2)a+aVB~1 MeV
Graph2
7.14101.3815.86
-4.9696.3336.27
-15.3391.8672.61
-19.6489.3788.64
-22.8188.98105.29
-27.0386.79115.26
-29.1286.9121.19
114.17.5-0.1
96.637.50.2
79.580.8-0.1
75.992.7-0.1
71.4102.10
68107.50
59.4113.80
51.6115.20
45.6116.30
41114.90
291033
111005.2
710416.2
310124.1
-1.697.527.7
-8.894.741.8
-6.994.847
-10.293.348.1
-9.491.756.4
-10.79459.2
18000.2
17800.3
17500.425
17300.475
17100.5
15900.75
14801
137.511.25
128.42.51.5
l=0
l=2
l=4
Ecm (MeV)
delta (degres)
rmat
exactn=0n=2n=4n=6n=8n=10
0.10.1211462936-0.3923295-2.1080656285-0.6801135367-0.4100695007-0.2809746661-0.2035934824
0.20.2936099368-0.7822122075-4.1813813407-1.3095784147-0.76902079-0.5107205499-0.3559167289
0.30.5683467314-1.1672526751-6.1875904061-1.8382252367-1.0261285601-0.6383777304-0.4060590674
0.40.9959065964-1.5451558686-8.0987455901-2.2164375151-1.1310770383-0.6134621025-0.3034756839
0.51.6269968041-1.9137718535-9.8926754258-2.3944443967-1.0332521913-0.38517601040.0026853892
0.62.5139105674-2.2711343232-11.5535915906-2.3204849346-0.67998926330.0992832080.5652323934
0.73.7130755026-2.6154916374-13.0719919023-1.9374647336-0.01343476850.89773741651.4418632351
0.85.2890422047-2.9453295488-14.4440270733-1.17756187381.03444666812.0777975172.6997939635
0.97.3204061398-3.2593853251-15.67054473060.04615064752.54949663743.72409155264.4227420887
19.908468563-3.5566534701-16.75601106831.85274913674.64696464165.94914902446.7213786861
1.113.1898957805-3.8363836717-17.70746299474.4141550417.48935427078.90991401499.7490608022
1.217.3550805661-4.0980719321-18.53358604817.988432806811.31397134612.832785978413.7254521098
1.322.6735750803-4.3414460539-19.243962238912.972340571216.473982569918.050084701818.970494583
1.429.5238994206-4.5664467636-19.848494760719.974479508823.490635592625.044905262725.9455198005
1.538.4078833659-4.7732057646-20.356993929429.866734221333.079761913534.471419642235.2710723586
1.649.8786006624-4.962021945-20.778897982143.594168220245.997082908647.020468786347.6048677225
1.764.2250973081-5.1333368332-21.123099703961.214358370962.363252524662.852096476763.1316317896
1.880.847666744-5.2877102337-21.397851863680.442939121480.592926591880.658223522680.6960296094
1.997.9660401155-5.4257967897-21.6107286197.66473776897.771649249697.819771764397.8481341158
2113.5983062531-5.548324037-21.7686247348111.1039258705111.9585552568112.3529400394112.5886720212
2.1126.8145869241-5.6560723415-21.8777791597121.1284134662123.0421160144123.9353077889124.4730691128
2.2137.7481018069-5.7498569582-21.9438127824128.7345645976131.7580721136133.1702303874134.0218695374
2.3146.9565142929-5.83051232-21.9717738025134.7788744038138.8917096414140.7999869783141.9483530665
2.4155.0136829985-5.8988785616-21.9661859126139.8720029105145.0582888343147.4358779097148.8596743525
2.5162.3927105801-5.9557902023-21.9310963864144.4502212515150.7199999038153.5464630781155.226886034
2.6169.4720561331-6.0020668565-21.8701222549148.8579781789156.2496638144159.5098611592161.4296839563
2.7176.5717622322-6.0385058008-21.7864935595153.418812038161.9935749131165.6708506496167.8097726715
2.8183.9909084796-6.0658762071-21.6830931962158.5080074386168.3329032436172.3953649425174.7213949937
2.9192.0406255117-6.084914842-21.5624932039164.6531919421175.7536871948180.126889295182.5809401709
3201.0702714858-6.0963230349-21.42698756172.7042262586184.9301583756189.4430417631191.9122698331
3.1211.4762258643-6.1007647231-21.278621662184.1094749318196.7813627125201.0739146365203.3541770171
3.2223.6614521364-6.0988653995-21.1192187396201.0612945984212.2850147304215.7329495099217.5147085496
3.3237.8852089901-6.0912117999-20.9504034653224.7998361555231.5321017078233.4763526553234.4706431653
3.4253.9711448227-6.078352188-20.7736230331250.6475738778252.3024869318252.7959870012253.0533324673
3.5271.0659230173-6.0607971105-20.5901659659271.0528021292271.0588427494271.0608052455271.0618680528
3.6287.8815687021-6.0390205152-20.4011788941284.7085655358286.068389703286.5407718773286.8052466909
3.7303.3933315447-6.0134611375-20.2076815247293.7614706087297.7289952257299.1488374582299.9591425346
3.8317.2621381123-5.9845240793-20.010580003300.0488049576307.0874782771309.6048629976311.0503083043
3.9329.6939210611-5.952582514-19.8106788431304.6532853761315.0834064101318.7271669589320.8109459356
4341.1297310459-5.9179794661-19.6086915873308.1854259264322.4573046081327.2311194904329.9272702578
4.1352.0553796897-5.8810296216-19.4052503348311.0001009733329.8530175902335.7599278107339.0266395037
4.2362.938395394-5.8420211373-19.2009142644313.3132833705337.9610252469344.9812131473348.7438551557
4.3374.2240287332-5.8012174203-18.9961772613315.2625254228347.6993822579355.6998980552359.7995502574
4.4386.3386730785-5.7588588605-18.7914747462316.9390888941360.4386950255368.9349153112373.0290872102
4.5399.6627278734-5.7151644995-18.5871897921318.4057231225378.0185392746385.7322374819389.1924981413
4.6414.4368554094-5.6703336261-18.3836586056319.7069281534401.2774113278406.1805425138408.2772307264
4.7430.5944377961-5.6245472925-18.181175442320.8751201962426.5035831985427.97980112428.6229202826
4.8447.6243602566-5.5779697455-17.9799970113321.9344714495447.5682386823447.5867651757447.5953645669
4.9284.6806239692-5.5307497725-17.7803464316322.9033798863282.823522825283.3836117103283.6588351392
5120.9746736451-5.4830219612-17.5824167764323.7961041072113.8479763039115.8729509965116.9014475676
rmat
0.1211462936-0.3923295-2.1080656285-0.6801135367-0.4100695007-0.2809746661-0.2035934824
0.2936099368-0.7822122075-4.1813813407-1.3095784147-0.76902079-0.5107205499-0.3559167289
0.5683467314-1.1672526751-6.1875904061-1.8382252367-1.0261285601-0.6383777304-0.4060590674
0.9959065964-1.5451558686-8.0987455901-2.2164375151-1.1310770383-0.6134621025-0.3034756839
1.6269968041-1.9137718535-9.8926754258-2.3944443967-1.0332521913-0.38517601040.0026853892
2.5139105674-2.2711343232-11.5535915906-2.3204849346-0.67998926330.0992832080.5652323934
3.7130755026-2.6154916374-13.0719919023-1.9374647336-0.01343476850.89773741651.4418632351
5.2890422047-2.9453295488-14.4440270733-1.17756187381.03444666812.0777975172.6997939635
7.3204061398-3.2593853251-15.67054473060.04615064752.54949663743.72409155264.4227420887
9.908468563-3.5566534701-16.75601106831.85274913674.64696464165.94914902446.7213786861
13.1898957805-3.8363836717-17.70746299474.4141550417.48935427078.90991401499.7490608022
17.3550805661-4.0980719321-18.53358604817.988432806811.31397134612.832785978413.7254521098
22.6735750803-4.3414460539-19.243962238912.972340571216.473982569918.050084701818.970494583
29.5238994206-4.5664467636-19.848494760719.974479508823.490635592625.044905262725.9455198005
38.4078833659-4.7732057646-20.356993929429.866734221333.079761913534.471419642235.2710723586
49.8786006624-4.962021945-20.778897982143.594168220245.997082908647.020468786347.6048677225
64.2250973081-5.1333368332-21.123099703961.214358370962.363252524662.852096476763.1316317896
80.847666744-5.2877102337-21.397851863680.442939121480.592926591880.658223522680.6960296094
97.9660401155-5.4257967897-21.6107286197.66473776897.771649249697.819771764397.8481341158
113.5983062531-5.548324037-21.7686247348111.1039258705111.9585552568112.3529400394112.5886720212
126.8145869241-5.6560723415-21.8777791597121.1284134662123.0421160144123.9353077889124.4730691128
137.7481018069-5.7498569582-21.9438127824128.7345645976131.7580721136133.1702303874134.0218695374
146.9565142929-5.83051232-21.9717738025134.7788744038138.8917096414140.7999869783141.9483530665
155.0136829985-5.8988785616-21.9661859126139.8720029105145.0582888343147.4358779097148.8596743525
162.3927105801-5.9557902023-21.9310963864144.4502212515150.7199999038153.5464630781155.226886034
169.4720561331-6.0020668565-21.8701222549148.8579781789156.2496638144159.5098611592161.4296839563
176.5717622322-6.0385058008-21.7864935595153.418812038161.9935749131165.6708506496167.8097726715
183.9909084796-6.0658762071-21.6830931962158.5080074386168.3329032436172.3953649425174.7213949937
192.0406255117-6.084914842-21.5624932039164.6531919421175.7536871948180.126889295182.5809401709
201.0702714858-6.0963230349-21.42698756172.7042262586184.9301583756189.4430417631191.9122698331
211.4762258643-6.1007647231-21.278621662184.1094749318196.7813627125201.0739146365203.3541770171
223.6614521364-6.0988653995-21.1192187396201.0612945984212.2850147304215.7329495099217.5147085496
237.8852089901-6.0912117999-20.9504034653224.7998361555231.5321017078233.4763526553234.4706431653
253.9711448227-6.078352188-20.7736230331250.6475738778252.3024869318252.7959870012253.0533324673
271.0659230173-6.0607971105-20.5901659659271.0528021292271.0588427494271.0608052455271.0618680528
287.8815687021-6.0390205152-20.4011788941284.7085655358286.068389703286.5407718773286.8052466909
303.3933315447-6.0134611375-20.2076815247293.7614706087297.7289952257299.1488374582299.9591425346
317.2621381123-5.9845240793-20.010580003300.0488049576307.0874782771309.6048629976311.0503083043
329.6939210611-5.952582514-19.8106788431304.6532853761315.0834064101318.7271669589320.8109459356
341.1297310459-5.9179794661-19.6086915873308.1854259264322.4573046081327.2311194904329.9272702578
puits carra=3, V0=-10
exact
n=0
n=2
n=4
n=6
n=8
n=10
k
dephasage
Sheet1 (2)
A1=4.0026N=200
A2=4.0026h=0.1
Z1=2
Z2=2
ell=0
E=1
hbar2/2m=20.9008
Emin=0.2
Emax=15180
pas=0.5
0.2178.404073368597.14101.3815.86
0.7159.292517745410.55-4.9696.3336.27
1.2137.419268523612.04-15.3391.8672.61
1.7119.519382243312.74-19.6489.3788.64
2.2104.736191003813.48-22.8188.98105.29
2.792.195943268114.24-27.0386.79115.26
3.281.314383385514.74-29.1286.9121.19
3.771.70336371561.92114.17.5-0.1
4.263.09628595652.6396.637.50.2
4.755.30293866753.23579.580.8-0.1
5.248.18308559723.4875.992.7-0.1
5.741.63035262093.73571.4102.10
6.235.5620677843.9468107.50
6.729.91256606524.43559.4113.80
7.224.6288740894.9451.6115.20
7.719.66749316195.4445.6116.30
8.214.9922752075.9441114.90
8.710.57282418146.15291033
9.26.38332218977.6111005.2
9.72.40164460988.9710416.2
10.2-1.39131385549.55310124.1
10.7-5.012185962710.2-1.697.527.7
11.2-8.475506262510.825-8.894.741.8
11.7-11.794083218710.9-6.994.847
12.2-14.979245757111.125-10.293.348.1
12.7-18.041064781711.405-9.491.756.4
13.2-20.988531581111.45-10.79459.2
13.7-23.82970596790.21800
14.2-26.57183987170.31780
14.7-29.22148117960.4251750
0.4751730
0.51710
0.751590
11480
1.25137.51
1.5128.42.5
0.1-122.3530270294.31640-118.0366270290.3-0.289583778
0.2-121.54815604654.30560-117.24255604650.6-0.3113767127
0.3-120.2184531044.28760-115.9308531040.9-0.0584835739
0.4-118.3812715334.26240-114.1188715331.20.2455904608
0.5-116.06037505494.230-111.83037505491.50.3814533243
0.6-113.28542628424.19040-109.09502628421.80.2920153029
0.7-110.09135601284.14360-105.94775601282.10.0593265422
0.8-106.51763201984.08960-102.42803201982.4-0.1998213058
0.9-102.60744878224.02840-98.57904878222.7-0.4064610099
1-98.40686130323.960-94.44686130323-0.5335289483
1.1-93.96388725513.88440-90.07948725513.3-0.5879826261
1.2-89.32760175433.80160-85.52600175433.6-0.5895346686
1.3-84.54724836283.71160-80.83564836283.9-0.5576925011
1.4-79.67138841533.61440-76.05698841534.2-0.5069334179
1.5-74.74710857993.510-71.23710857994.5-0.446409599
1.6-69.81930380323.39840-66.42090380324.8-0.3812730173
1.7-64.93004959343.27960-61.65044959345.1-0.3141438166
1.8-60.11807411273.15360-56.96447411275.4-0.2462211564
1.9-55.41833691973.02040-52.39793691975.7-0.1779892301
2-50.86171758772.880-47.98171758776-0.1096171181
2.1-46.47481394752.74285714290-43.73195680466.3-0.0411643367
2.2-42.2798464952.61818181820-39.66166467686.60.0273236268
2.3-38.29466265922.50434782610-35.79031483316.90.0957764759
2.4-34.53283222932.40-32.13283222937.20.1640869118
2.5-31.00382333662.3040-28.69982333667.50.2321097021
2.6-27.71324701092.21538461540-25.49786239557.80.2996648609
2.7-24.66315748562.13333333330-22.52982415238.10.3665419583
2.8-21.8523950832.05714285710-19.79525222598.40.4325044934
2.9-19.2769586491.98620689660-17.29075175248.70.4972940401
3-16.93039505221.920-15.010395052290.5606341488
3.1-14.80419416751.85806451610-12.94612965149.30.6222340541
3.2-12.88817894391.80-11.08817894399.60.6817922416
3.3-11.17088154031.74545454550-9.42542699499.90.7389999078
3.4-9.63989802571.69411764710-7.945780378610.20.7935443388
3.5-8.28221570911.64571428570-6.636501423410.50.8451122162
3.6-7.08450872311.60-5.484508723110.80.8933928544
3.7-6.03339898071.55675675680-4.476642223911.10.9380813677
3.8-5.115681011.51578947370-3.599891536311.40.9788817594
3.9-4.31851041011.47692307690-2.841587333211.71.0155099246
4-3.62955673891.440-2.1895567389121.0476965539
4.1-3.0371225281.40487804880-1.632244479212.31.0751899253
4.2-2.53023081631.37142857140-1.158802244912.61.0977585695
4.3-2.09868410221.33953488370-0.759149218512.91.1151937928
4.4-1.73309795121.30909090910-0.424007042113.21.1273120422
4.5-1.42491267381.280-0.144912673813.51.1339570967
4.6-1.16638652591.25217391300.085787387213.81.1350020698
4.7-0.95057380671.225531914900.274958108214.11.1303512067
4.8-0.77129105791.200.428708942114.41.1199414636
4.9-0.62307432241.175510204100.552435881714.71.103743855
5-0.50113013071.15200.6508698693151.0817645565
5.1-0.40128255671.129411764700.72812920815.31.0540457531
5.2-0.31991835071.107692307700.78777395715.61.0206662234
5.3-0.25393182091.086792452800.832860631915.90.9817416515
5.4-0.2006708111.066666666700.865995855716.20.9374246625
5.5-0.15788482471.047272727300.889387902616.50.8879045753
5.6-0.12367607011.028571428600.904895358516.80.8334068731
5.7-0.09645396131.010526315800.914072354517.10.7741923898
5.8-0.0748934030.993103448300.918210045317.40.7105562157
5.9-0.05789701390.976271186400.918374172617.70.6428263261
6-0.04456130180.9600.9154386982180.57136194
6.1-0.03414669520.944262295100.910115599818.30.4965516161
6.2-0.02605125150.929032258100.902981006618.60.4188110987
6.3-0.01978780440.914285714300.894497909918.90.3385809239
6.4-0.01496427670.900.885035723319.20.2563238032
6.5-0.01126686150.886153846200.874886984619.50.1725217984
6.6-0.00844577070.872727272700.86428150219.80.0876733092
6.7-0.00630325270.859701492500.853398239820.10.0022898911
6.8-0.00468359420.847058823500.842375229320.4-0.0831070737
6.9-0.00346483780.834782608700.831317770920.7-0.1679898295
7-0.00255197050.822857142900.820305172321-0.2518277995
7.1-0.00187136070.811267605600.809396244921.3-0.3340912133
7.2-0.00136624460.800.798633755421.6-0.4142547816
7.3-0.00099308980.789041095900.788048006121.9-0.4918013926
7.4-0.00071868350.778378378400.777659694922.2-0.5662258015
7.5-0.00051781660.76800.767482183422.5-0.6370382853
7.6-0.00037145250.757894736800.757523284322.8-0.703768236
7.7-0.00026528930.748051948100.747786658723.1-0.7659676626
7.8-0.00018863640.738461538500.738272902123.4-0.8232145765
7.9-0.00013354270.729113924100.728980381423.7-0.8751162316
8-0.00009412480.7200.719905875224-0.9213121939
8.1-0.00006605060.711111111100.711045060524.3-0.9614772153
8.2-0.00004614650.702439024400.702392877924.6-0.9953238875
8.3-0.00003209890.693975903600.693943804724.9-1.0226050532
8.4-0.00002222950.685714285700.685692056225.2-1.0431159547
8.5-0.00001532710.677647058800.677631731725.5-1.0566960984
8.6-0.00001052150.669767441900.669756920425.8-1.0632308212
8.7-0.00000719090.662068965500.662061774626.1-1.06265254
8.8-0.00000489310.654545454500.654540561526.4-1.0549416744
8.9-0.00000331490.647191011200.647187696426.7-1.0401272303
9-0.00000223580.6400.639997764227-1.0182870361
9.1-0.00000150140.63296703300.632965531527.3-0.9895476274
9.2-0.00000100380.626086956500.626085952727.6-0.9540837759
9.3-0.00000066820.619354838700.619354170527.9-0.9121176624
9.4-0.00000044280.612765957400.612765514628.2-0.8639176972
9.5-0.00000029220.606315789500.606315497328.5-0.8097969918
9.6-0.00000019190.600.599999808128.8-0.7501114913
9.7-0.00000012550.59381443300.593814307529.1-0.6852577759
9.8-0.00000008170.58775510200.587755020329.4-0.6156705474
9.9-0.0000000530.581818181800.581818128829.7-0.5418198135
10-0.00000003420.57600.575999965830-0.4642077907
10.1-0.0000000220.570297029700.570297007730.3-0.3833655444
10.2-0.00000001410.564705882400.564705868330.6-0.2998493896
10.3-0.0000000090.55922330100.55922329230.9-0.2142370768
10.4-0.00000000570.553846153800.553846148231.2-0.1271237903
10.5-0.00000000360.548571428600.54857142531.5-0.0391179861
10.6-0.00000000230.543396226400.543396224231.80.0491629002
10.7-0.00000000140.53831775700.538317755632.10.1370968443
10.8-0.00000000090.533333333300.533333332532.40.2240616917
10.9-0.00000000050.52844036700.528440366432.70.3094396497
11-0.00000000030.523636363600.5236363633330.3926217808
11.1-0.00000000020.518918918900.518918918733.30.4730124629
11.2-0.00000000010.514285714300.514285714233.60.5500337829
11.3-0.00000000010.509734513300.509734513233.90.6231298302
11.4-00.505263157900.505263157834.20.6917708574
11.5-00.500869565200.500869565234.50.755457275
11.6-00.496551724100.496551724134.80.81372345
11.7-00.492307692300.492307692335.10.8661412775
11.8-00.488135593200.488135593235.40.9123234974
11.9-00.484033613400.484033613435.70.9519267288
12-00.4800.48360.9846541975
12.1-00.476033057900.476033057836.31.0102581345
12.2-00.472131147500.472131147536.61.028541824
12.3-00.468292682900.468292682936.91.0393612841
12.4-00.46451612900.46451612937.21.0426265646
12.5-00.460800.460837.51.0383026494
12.6-00.457142857100.457142857137.81.0264099547
12.7-00.453543307100.453543307138.11.0070244161
12.8-00.4500.4538.40.9802771614
12.9-00.446511627900.446511627938.70.9463537697
13-00.443076923100.4430769231390.9054931189
13.1-00.439694656500.439694656539.30.8579858278
13.2-00.436363636400.436363636439.60.8041723039
13.3-00.433082706800.433082706839.90.7444404069
13.4-00.429850746300.429850746340.20.6792227451
13.5-00.426666666700.426666666740.50.6089936229
13.6-00.423529411800.423529411840.80.5342656596
13.7-00.420437956200.420437956241.10.455586105
13.8-00.417391304300.417391304341.40.3735328767
13.9-00.414388489200.414388489241.70.2887103484
14-00.411428571400.4114285714420.2017449194
14.1-00.408510638300.408510638342.30.1132803997
14.2-00.405633802800.405633802842.60.0239732413
14.3-00.402797202800.402797202842.9-0.0655123443
14.4-00.400.443.2-0.1545093495
14.5-00.397241379300.397241379343.5-0.2423529754
14.6-00.394520547900.394520547943.8-0.3283856403
14.7-00.391836734700.391836734744.1-0.4119619541
14.8-00.389189189200.389189189244.4-0.4924536201
14.9-00.386577181200.386577181244.7-0.5692542262
15-00.38400.38445-0.6417838889
15.1-00.381456953600.381456953645.3-0.7094937132
15.2-00.378947368400.378947368445.6-0.7718700337
15.3-00.376470588200.376470588245.9-0.8284384036
15.4-00.37402597400.37402597446.2-0.8787672995
15.5-00.371612903200.371612903246.5-0.9224715127
15.6-00.369230769200.369230769246.8-0.9592151988
15.7-00.366878980900.366878980947.1-0.9887145627
15.8-00.36455696200.36455696247.4-1.0107401536
15.9-00.362264150900.362264150947.7-1.0251187542
16-00.3600.3648-1.0317348456
16.1-00.357763975200.357763975248.3-1.0305316352
16.2-00.355555555600.355555555648.6-1.0215116394
16.3-00.353374233100.353374233148.9-1.0047368124
16.4-00.351219512200.351219512249.2-0.9803282209
16.5-00.349090909100.349090909149.5-0.9484652638
16.6-00.346987951800.346987951849.8-0.9093844411
16.7-00.344910179600.344910179650.1-0.8633776813
16.8-00.342857142900.342857142950.4-0.8107902367
16.9-00.340828402400.340828402450.7-0.752018163
17-00.338823529400.338823529451-0.6875054001
17.1-00.336842105300.336842105351.3-0.6177404747
17.2-00.334883720900.334883720951.6-0.5432528514
17.3-00.332947976900.332947976951.9-0.4646089559
17.4-00.331034482800.331034482852.2-0.3824079031
17.5-00.329142857100.329142857152.5-0.2972769597
17.6-00.327272727300.327272727352.8-0.2098667777
17.7-00.325423728800.325423728853.1-0.1208464334
17.8-00.323595505600.323595505653.4-0.0308983107
17.9-00.321787709500.321787709553.70.0592871325
18-00.3200.32540.1490166742
18.1-00.318232044200.318232044254.30.2375996734
18.2-00.316483516500.316483516554.60.3243534097
18.3-00.314754098400.314754098454.90.4086083749
18.4-00.313043478300.313043478355.20.4897134752
18.5-00.311351351400.311351351455.50.5670411044
18.6-00.309677419400.309677419455.80.6399920468
18.7-00.308021390400.308021390456.10.7080001718
18.8-00.306382978700.306382978756.40.7705368828
18.9-00.304761904800.304761904856.70.8271152846
19-00.303157894700.3031578947570.8772940371
19.1-00.301570680600.301570680657.30.9206808625
19.2-00.300.357.60.956935679
19.3-00.298445595900.298445595957.90.9857733354
19.4-00.296907216500.296907216558.21.0069659231
19.5-00.295384615400.295384615458.51.020344647
19.6-00.29387755100.29387755158.81.0258012398
19.7-00.292385786800.292385786859.11.0232889062
19.8-00.290909090900.290909090959.41.0128227896
19.9-00.289447236200.289447236259.70.9944799553
20-00.28800.288600.9683988902
60.300.095522388100.0955223881
60.600.09504950500.095049505
60.900.094581280800.0945812808
61.200.094117647100.0941176471
61.500.093658536600.0936585366
61.800.093203883500.0932038835
62.100.092753623200.0927536232
62.400.092307692300.0923076923
62.700.091866028700.0918660287
6300.091428571400.0914285714
63.300.090995260700.0909952607
63.600.090566037700.0905660377
63.900.090140845100.0901408451
64.200.089719626200.0897196262
64.500.089302325600.0893023256
64.800.088888888900.0888888889
65.100.088479262700.0884792627
65.400.088073394500.0880733945
65.700.087671232900.0876712329
6600.087272727300.0872727273
66.300.086877828100.0868778281
66.600.086486486500.0864864865
66.900.086098654700.0860986547
67.200.085714285700.0857142857
67.500.085333333300.0853333333
67.800.084955752200.0849557522
68.100.084581497800.0845814978
68.400.084210526300.0842105263
68.700.083842794800.0838427948
6900.083478260900.0834782609
69.300.083116883100.0831168831
69.600.082758620700.0827586207
69.900.082403433500.0824034335
70.200.082051282100.0820512821
70.500.081702127700.0817021277
70.800.081355932200.0813559322
71.100.081012658200.0810126582
71.400.080672268900.0806722689
71.700.08033472800.080334728
7200.0800.08
72.300.079668049800.0796680498
72.600.07933884300.079338843
72.900.079012345700.0790123457
73.200.078688524600.0786885246
73.500.078367346900.0783673469
73.800.078048780500.0780487805
74.100.077732793500.0777327935
74.400.077419354800.0774193548
74.700.077108433700.0771084337
7500.076800.0768
75.300.076494023900.0764940239
75.600.076190476200.0761904762
75.900.075889328100.0758893281
76.200.075590551200.0755905512
76.500.075294117600.0752941176
76.800.07500.075
77.100.074708171200.0747081712
77.400.074418604700.0744186047
77.700.074131274100.0741312741
7800.073846153800.0738461538
78.300.073563218400.0735632184
78.600.073282442700.0732824427
78.900.073003802300.0730038023
79.200.072727272700.0727272727
79.500.072452830200.0724528302
79.800.072180451100.0721804511
80.100.071910112400.0719101124
80.400.07164179100.071641791
80.700.071375464700.0713754647
8100.071111111100.0711111111
81.300.070848708500.0708487085
81.600.070588235300.0705882353
81.900.070329670300.0703296703
82.200.070072992700.0700729927
82.500.069818181800.0698181818
82.800.069565217400.0695652174
83.100.069314079400.0693140794
83.400.069064748200.0690647482
83.700.068817204300.0688172043
8400.068571428600.0685714286
84.300.068327402100.0683274021
84.600.068085106400.0680851064
84.900.06784452300.067844523
85.200.067605633800.0676056338
85.500.067368421100.0673684211
85.800.067132867100.0671328671
86.100.066898954700.0668989547
86.400.066666666700.0666666667
86.700.066435986200.0664359862
8700.066206896600.0662068966
87.300.065979381400.0659793814
87.600.065753424700.0657534247
87.900.065529010200.0655290102
88.200.065306122400.0653061224
88.500.065084745800.0650847458
88.800.064864864900.0648648649
89.100.064646464600.0646464646
89.400.064429530200.0644295302
89.700.064214046800.0642140468
9000.06400.064
Sheet1 (2)
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
000
000
000
000
000
000
l=0
l=2
l=4
Ecm (MeV)
delta (degres)
dep
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
r (fm)
V(r) (MeV)
puits carre
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
r (fm)
V(r) (MeV)
Sheet1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
r (fm)
fonction d'onde
fig_dep
k0^2=100001.85302213693.49381077914.8138334163180100001.85302213693.49381077914.8138334163
a=31500002.68453231684.2629792587
2000001.48550118143.6294616901
25000002.8588445498
0.1-179.878853912-179.8788539120.12114629370-100.1-0.17710230230.090092697800
0.2-179.7063902686-179.70639026860.29360993713-100.2-0.34860549690.179452650800101.51789327692.56144490473.0357865538
0.3-179.4316534737-179.43165347370.568346732300.3-0.50908749240.267353073900151.006975672.63362867543.36949551123.7567938458
0.4-179.0040936082-179.00409360820.99590659750.4-0.65347463380.353079052500202.32551069663.44354468534.0696437194.3826932359
0.5-178.3730033997-178.37300339971.6269968060-1.86050.5-0.77720210650.435933357400251.43.154.054.6
0.6-177.4860896354-177.48608963542.51391057023-1.86050.6-0.87635825370.5152421153002015251012
0.7-176.286924699-176.2869246993.71307550670.7-0.94780824330.5903602899000.1181.4677250619177.960772046359.02533361160.12114629372.4206818193
0.8-174.710957995-174.7109579955.28904221060-4.2320.8-0.98929317660.6606769275000.2182.991425716176.0282823554358.0876004190.29360993714.9632137118
0.9-172.6795940578-172.67959405787.32040614793-4.2320.9-0.9995015030.7256201266000.3184.6306289674174.2960852553357.22158805350.5683467327.7610646265
1-170.0915316316-170.09153163169.90846857411-0.97811048530.7846616893000.4186.4525440843172.8352836479356.45815331930.995906597510.9732459508
1.1-166.8101044105-166.810104410513.1898957951001.1-0.92579640260.8373214167000.5188.5374794108171.6911653169355.82306040061.62699680614.803215047
1.2-162.6449192088197.355080791217.3550805855301.2-0.84421317020.8831710151000.6190.9865344084170.8852625167355.33655164622.513910570219.5257951172
1.3-157.3264246888202.673575311222.67357510561.3-0.73594005050.9218375792000.7193.933041482170.4207956333355.01360666973.713075506725.5236760624
1.4-150.4761003408209.523899659229.5238994535001.4-0.60440010940.9530066248000.8197.5599224122170.2892464653354.86473906475.289042210633.32465615
1.5-141.5921163857218.407883614338.4078834087301.5-0.45375199590.9764246468000.9202.1256891894170.476463032354.89713878587.320406147943.5895168752
1.6-130.1213990763229.878600923749.8786007181.6-0.28875846570.9919011811001208.0004563179170.9675542999355.11598401839.908468574156.89243193
1.7-115.7749024147244.225097585364.22509737971.7-0.11463580660.9993103534001.1215.7028631155171.7504870203355.525797365713.189895795173.0631620291
1.8-99.1523329603260.847667039780.8476668341.80.06311107560.9985919032001.2225.8869661673172.8186568489356.131785388817.355080585590.4563910372
1.9-82.0339595646277.9660404354-82.03395997591.90.23886269440.9897516738001.3239.1186845724174.1728456433356.941163562122.6735751056106.6096691023
2-66.4016934095293.5983065905-66.401693820920.40706264440.9728615649001.4255.2095654332175.8230047822357.964525671829.5238994535120.0359917726
2.1-53.1854131351-53.1854131351-53.18541313512.10.56239326640.9480589475001.5272.4858795976177.7903068106359.217370661938.4078834087130.6853035126
2.2-42.2518982402-42.2518982402-42.25189824022.20.69994376660.9155455472001.6288.4698226076180.1099415492360.721960052749.878600718139.1631493861
2.3-33.0434857439-33.0434857439-33.04348574392.30.81536547180.875585803001.7301.6819764517182.8352362061362.509759566664.2250973797146.1220119282
2.4-24.9863170293-24.9863170293-24.98631702932.40.90500931260.8285047167001.8312.0823312095186.0438806373364.62483981680.847666834152.0756726533
2.5-17.6072894395-17.6072894395-17.60728943952.50.96604118970.7746852097001.9320.2777735488189.8473471048367.128800979197.9660400241157.3980609907
2.6-10.5279438786-10.5279438786-10.52794387862.60.9965315740.7145650085002326.9158843901194.4049217817370.1080801075113.5983061791162.3629802757
2.7-3.4282377717-3.4282377717-3.42823777172.70.99551650870.6486330846002.1332.5024970526199.9436452137373.6849189144126.8145868649167.1816713603
2.83.9909082784-176.00909172163.99090848412.80.96302808520.5774256776002.2337.4015061311206.7831086446378.0337289045137.7481017598172.0315921239
2.912.0406253194-167.959374680612.04062552512.90.90009342850.5015219339002.3341.8741995566215.353796351383.4045311164146.9565142561177.0786933062
321.0702713036-158.929728696421.070271509330.80870222420.4215391962002.4346.115709766226.165639965390.1522895111155.0136829707182.4966413043
3.131.4762256937-148.523774306331.47622589943.10.70637669520.3435430891002.5350.2820850724239.6174556492398.757705339162.3927105605188.4859353816
3.243.6614519794-136.338548020643.6614521853.20.61699847060.279978363002.6354.5101233997255.5272763612409.7824638596169.4720561214195.2947146756
3.357.8852088489-122.114791151157.88520905463.30.53892932110.2281748236002.7358.9331797519272.6555961753423.6163452932176.5717622283203.2399147979
3.473.9711446994-106.028855300673.97114490513.40.47073830310.1859563345002.8363.695762642289.1030748364439.8901171024183.9909084841212.7179028552
3.591.0659229182-88.9340770818-88.93407708183.50.41117553150.1515494032002.9368.9693142959303.5250010401457.0146962842192.0406255251224.1688655506
3.6107.8815686217-72.1184313783-72.11843137833.60.35914926950.1235086811003374.9711159554315.6593489961472.9091534118201.0702715093237.9165334555
3.7123.3933314816-56.6066685184-56.60666851843.70.31370591860.1006562479003.1381.9867657431325.9007944155486.3815094536211.4762258994253.8139692577
3.8137.2621380647-42.7378619353-42.73786193533.80.27401253930.0820321305003.2390.3909446006334.8066820812497.4002608639223.661452185270.8970682855
3.9149.6939210273-30.3060789727-30.30607897273.90.23934158480.0668539765003.3400.6429935255342.8840425261506.480233649237.8852090546287.6375543062
4161.1297310249-18.8702689751-18.870268975140.20905756490.0544841899003.4413.1907110947350.5536027779514.2001516944253.9711449051302.8270562582
4.1172.0553796808-7.9446203192-7.94462031924.10.18260539830.044403147003.5428.1707124938358.1743693809521.0406591276271.0659229182316.0984259068
4.2182.9383951916-177.06160480842.93839539734.20.15950023870.0361873687003.6444.935082861366.0802990503527.3753115006287.8815686217327.7089975665
4.3194.2240285434-165.775971456614.2240287494.30.13931858740.0294917306003.7461.9554239484374.6149806696533.5026783152303.3933314816338.1467805602
4.4206.3386729022-153.661327097826.33867310794.40.12169053130.024034966003.8477.6398889859384.1579075212539.6819518571317.2621380647347.9144943179
4.5219.6627277119-140.337272288139.66272791754.50.10629296270.0195878498003.9491.2344717922395.1271708682546.1648524118329.6939210273357.4712301529
4.6234.4368552644-125.563144735654.43685547014.60.09284365670.0159635699004502.8302630771407.9191162319553.224895519341.1297310249367.2419298069
4.7250.5944376691-109.405562330970.59443787484.70.08109609870.0130098794004.1512.8970769281422.7210817812561.1849298501352.0553796808377.6423163235
4.8267.6243601486-92.375639851487.62436035424.80.07083496560.0106027013004.2521.9574430472439.1997558214570.4373003662362.9383953973389.0910372838
4.9284.6806238853-75.3193761147-75.31937611474.90.06187217910.0086409159004.3530.4772889939456.3425709643581.4320984524374.224028749401.978758649
5300.9746735794-59.0253264206-59.025326420650.05404345890.0070421137004.4538.863000318472.8579906068594.5702372959386.3386731079416.5516346866
5.10.04720531090.005739133004.5547.4913070621487.8804222189609.913481299399.6627279175432.6955675119
5.20.04123239740.0046772388004.6556.7429696699501.2382426723626.7854968522414.4368554701449.7601846532
5.30.03601523990.0038118236004.7567.026128021513.2239187777643.7695348378430.5944378748466.7183414728
5.40.03145821220.0031065335004.8578.7673876552524.300658851659.4627504664447.6243603542482.6773520086
5.50.02747778760.0025317411004.9592.3246175693534.9502566349673.2197351418464.6806238853497.2617905877
5.60.02400100830.0020633008005607.7669889165545.6325526936685.1372181285480.9746735794510.5818335586
5.70.02096414780.001681534600
5.80.01831154280.001370405400
5.90.01599457340.001116843500
60.01397077140.000910197400
6.10.01220304220.000741786300
6.20.01065898470.000604535900
6.30.00931029760.000492680400
6.40.00813226060.000401521300
6.50.00710328130.00032722900
6.60.00620449930.000266682900
6.70.00541944060.000217339300
6.80.00473371590.000177125700
6.90.00413475620.000144352700
70.00361158330.000117643500
7.10.00315460770.000095876300
7.20.00275545350.000078136600
7.30.00240680450.000063679200
7.40.00210227020.000051896900
7.50.00183626880.000042294500
7.60.00160392470.000034468900
7.70.00140097930.000028091200
7.80.00122371260.000022893600
7.90.00106887560.000018657700
80.00093363020.000015205500
8.10.00081549750.000012392100
8.20.00071231210.000010099200
8.30.00062218290.000008230600
8.40.00054345780.000006707700
8.50.00047469370.000005466600
8.60.00041463050.000004455100
8.70.00036216710.000003630800
8.80.00031634190.00000295900
8.90.0002763150.000002411500
90.00024135270.000001965300
9.10.00021081420.000001601700
9.20.00018413980.000001305300
9.30.00016084050.000001063800
9.40.00014048920.00000086700
9.50.00012271310.000000706600
9.60.00010718610.000000575800
9.70.00009362380.000000469300
9.80.00008177750.000000382500
9.90.00007143020.000000311700
100.00006239210.00000025400
fig_dep
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
0
0
0
0
0
0
0
0
coulomb
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
20
15
25
10
12
00.019648748
0.01-0.1427067336-10099.85729326640-10.10.07549100070000
0.02-0.1431874888-5049.85681251123-10.20.15055117170000
0.03-0.1439893604-33.333333333333.189343973300.30.22475214210000
0.04-0.1451132707-2524.85488672930.40.29767044450000
0.05-0.1465605179-20-2.3040-0.43560.50.36888993150000
0.06-0.1483327817-16.666666666716.51833388493-0.43560.60.43800415130000
0.07-0.1504321327-14.285714285714.1352821530.70.50461866660000
0.08-0.1528610421-12.5-6.561000.80.56835330620000
0.09-0.1556223947-11.111111111110.9554887164300.90.62884433420000
0.1-0.1587195034-109.841280496610.68574652650000
0.11-0.1621561263-9.0909090909-9.216001.10.73873514010000
0.12-0.165936486-8.33333333338.1673968473301.20.78750776740000
0.13-0.1700652918-7.69230769237.52224240051.30.83178606120000
0.14-0.1745477642-7.14285714296.9683093787001.40.8713173240000
0.15-0.1793896624-6.66666666676.4872770042301.50.90587594940000
0.16-0.1845973156-6.256.06540268441.60.93526471010000
0.17-0.1901776566-5.88235294125.692175284601.70.95931588360000
0.18-0.1961382601-5.55555555565.359417295501.80.9778922090000
0.19-0.2024873846-5.26315789475.06067051021.90.99088767050000
0.2-0.2092340185-54.790765981520.99822810270000
0.21-0.2163879318-4.76190476194.54551683012.10.99987161340000
0.22-0.223959732-4.54545454554.32149481342.20.99580882310000
0.23-0.2319609272-4.3478260874.11586515982.30.98606291820000
0.24-0.2404039944-4.16666666673.92626267222.40.97068951890000
0.25-0.2493024562-43.75069754382.50.94977636180000k0^2=1
0.26-0.2586709645-3.84615384623.58748288172.60.9234427990000a=3
0.27-0.2685253941-3.70370370373.43517830962.70.89183911690000
0.28-0.2788829455-3.57142857143.2925456262.80.85514567890000racines=0.66
0.29-0.2897622596-3.44827586213.15851360252.90.81357189570000
0.3-0.3011835448-3.33333333333.032149788530.76735503020000
0.31-0.3131687181-3.22580645162.91263773353.10.71870398980000
0.32-0.3257415626-3.1252.79925843743.20.67313747170000
0.33-0.3389279032-3.03030303032.69137512723.30.63045991440000
0.34-0.3527558028-2.94117647062.58842066773.40.59048815480000
0.35-0.3672557826-2.85714285712.48988707453.50.55305064290000
0.36-0.3824610682-2.77777777782.39531670953.60.5179867050000
0.37-0.3984078677-2.70270270272.3042948353.70.48514585410000
0.38-0.4151356842-2.63157894742.21644326313.80.45438714450000
0.39-0.4326876698-2.56410256412.13141489433.90.42557856640000
0.4-0.4511110257-2.52.048888974340.39859647960000
0.41-0.470457457-2.43902439021.96856693334.10.37332508280000
0.42-0.490783691-2.3809523811.89016868994.20.34965591670000
0.43-0.5121520691-2.32558139531.81342932634.30.32748739830000
0.44-0.5346312237-2.27272727271.7380960494.40.30672438510000
0.45-0.5582968583-2.22222222221.66392536394.50.28727776670000
0.46-0.5832326448-2.17391304351.59068039874.60.26906408240000
0.47-0.609531263-2.12765957451.51812831154.70.25200516310000
0.48-0.6372956075-2.08333333331.44603772584.80.23602779550000
0.49-0.6666401944-2.04081632651.37417613214.90.22106340830000
0.5-0.6976928076-21.302307192450.20704777750000
0.51-0.7305964346-1.96078431371.23018787915.10.1939207510000
0.52-0.7655115512-1.92307692311.15756537185.20.18162599060000
0.53-0.8026188326-1.88679245281.08417362025.30.17011072960000
0.54-0.8421223856-1.85185185191.00972946635.40.15932554720000
0.55-0.884253623-1.81818181820.93392819525.50.14922415570000
0.56-0.9292759343-1.78571428570.85643835145.60.13976320190000
0.57-0.97749035-1.75438596490.77689561495.70.13090208170000
0.58-1.0292424555-1.7241379310.69489547555.80.12260276490000
0.59-1.0849308889-1.69491525420.60998436535.90.11482963280000
0.6-1.1450178621-1.66666666670.521648804660.10754932460000
0.61-1.2100422902-1.63934426230.42930197216.10.10073059490000
0.62-1.2806363183-1.61290322580.33226690756.20.09434417920000
0.63-1.3575463141-1.58730158730.22975527326.30.08836266830000
0.64-1.4416598043-1.56250.12084019576.40.08276039090000
0.65-1.5340404121-1.53846153850.00442112646.50.07751330320000
0.66-1.6359737151-1.5151515152-0.12082226.60.07259888590000
0.67-1.7490282248-1.4925373134-0.25649091136.70.06799604730000
0.68-1.8751376408-1.4705882353-0.40454940556.80.06368503310000
0.69-2.0167135784-1.4492753623-0.5674382166.90.05964734130000
0.7-2.1768028017-1.4285714286-0.748231373170.0558656430000
0.71-2.3593109122-1.4084507042-0.9508602087.10.0523237080000
0.72-2.5693277391-1.3888888889-1.18043885027.20.0490063350000
0.73-2.8136128052-1.3698630137-1.44374979157.30.04589928670000
0.74-3.101340944-1.3513513514-1.74998959267.40.04298922810000
0.75-3.4452866674-1.3333333333-2.1119533347.50.04026367010000
0.76-3.86378124-1.3157894737-2.54799176647.60.0377109150000
0.77-4.3841023727-1.2987012987-3.0854010747.70.03532000710000
0.78-5.0486900342-1.2820512821-3.76663875217.80.0330806850000
0.79-5.9273809657-1.2658227848-4.66155818097.90.0309833380000
0.8-7.1437694577-1.25-5.893769457780.02901896480000
0.81-8.9392578084-1.2345679012-7.70468990718.10.02717913480000
0.82-11.8573329753-1.2195121951-10.63782078028.20.02545595170000
0.83-17.431217263-1.2048192771-16.22639798598.30.02384202010000
0.84-32.3198366239-1.1904761905-31.12936043348.40.02233041330000
0.85-198.7343696838-1.1764705882-197.55789909568.50.02091464380000
0.8649.0705648971-1.162790697750.23335559488.60.01958863550000
0.8722.0698200915-1.149425287423.21924537888.70.01834669730000
0.8814.330219272-1.136363636415.46658290848.80.01718349920000
0.8910.6595921917-1.123595505611.78318769738.90.0160940490000
0.98.5166803778-1.11111111119.627791488990.01507367090000
0.917.1117602012-1.09890109898.21066130019.10.01411798580000
0.926.1194125708-1.08695652177.20636909259.20.01322289210000
0.935.3810253855-1.07526881726.45629420279.30.01238454810000
0.944.8100545281-1.06382978725.87388431549.40.0115993560000
0.954.3552676114-1.05263157895.40789919039.50.01086394570000
0.963.9844012449-1.04166666675.02606791159.60.01017516120000
0.973.6761257016-1.03092783514.70705353669.70.00953004630000
0.983.4157751164-1.02040816334.43618327969.80.00892583230000
0.993.1929336493-1.01010101014.20303465949.90.0083599260000
1.6666666667-42.6934676102-0.6100.00782989870000
1.683333333316.5816923418-0.5940594059
1.76.9059512077-0.5882352941
1.71666666674.3456366117-0.5825242718
1.73333333333.1615156156-0.5769230769
1.752.4787589294-0.5714285714
1.76666666672.0343729174-0.5660377358
1.78333333331.7219221753-0.5607476636
1.81.4901234499-0.5555555556
1.81666666671.3112194095-0.5504587156
1.83333333331.1688760386-0.5454545455
1.851.0528542759-0.5405405405
1.86666666670.9564096274-0.5357142857
1.88333333330.8749184376-0.5309734513
1.90.8051049437-0.5263157895
1.91666666670.7445834019-0.5217391304
1.93333333330.6915749812-0.5172413793
1.950.6447262533-0.5128205128
1.96666666670.6029891441-0.5084745763
1.98333333330.5655393621-0.5042016807
20.5317196469-0.5
2.01666666670.5009994503-0.4958677686
2.03333333330.472945756-0.4918032787
2.050.447201604-0.487804878
2.06666666670.4234700471-0.4838709677
2.08333333330.4015020009-0.48
2.10.3810869272-0.4761904762
2.11666666670.3620456088-0.4724409449
2.13333333330.3442244874-0.46875
2.150.3274911835-0.4651162791
2.16666666670.3117309197-0.4615384615
2.18333333330.2968436417-0.4580152672
2.20.2827416831-0.4545454545
2.21666666670.2693478564-0.4511278195
2.23333333330.2565938836-0.447761194
2.250.2444190956-0.4444444444
2.26666666670.2327693499-0.4411764706
2.28333333330.2215961224-0.4379562044
2.30.2108557428-0.4347826087
2.31666666670.2005087468-0.4316546763
2.33333333330.1905193236-0.4285714286
2.350.180854844-0.4255319149
2.36666666670.1714854526-0.4225352113
2.38333333330.1623837163-0.4195804196
2.40.1535243177-0.4166666667
2.41666666670.1448837868-0.4137931034
2.43333333330.1364402649-0.4109589041
2.450.128173296-0.4081632653
2.46666666670.1200636392-0.4054054054
2.48333333330.1120931019-0.4026845638
2.50.1042443867-0.4
2.51666666670.0965009532-0.3973509934
2.53333333330.0888468884-0.3947368421
2.550.0812667869-0.3921568627
2.56666666670.0737456365-0.3896103896
2.58333333330.0662687094-0.3870967742
2.60.0588214553-0.3846153846
2.61666666670.0513893965-0.3821656051
2.63333333330.043958022-0.3797468354
2.650.0365126803-0.3773584906
2.66666666670.0290384678-0.375
2.68333333330.0215201118-0.3726708075
2.70.0139418455-0.3703703704
2.71666666670.0062872729-0.3680981595
2.7333333333-0.0014607784-0.3658536585
2.75-0.0093204213-0.3636363636
2.7666666667-0.0173108924-0.3614457831
2.7833333333-0.0254527585-0.3592814371
2.8-0.033768153-0.3571428571
2.8166666667-0.0422810474-0.3550295858
2.8333333333-0.051017566-0.3529411765
2.85-0.0600063533-0.350877193
2.8666666667-0.0692790067-0.3488372093
2.8833333333-0.0788705876-0.3468208092
2.9-0.0888202331-0.3448275862
2.9166666667-0.099171888-0.3428571429
2.9333333333-0.1099751925-0.3409090909
2.95-0.1212865619-0.3389830508
2.9666666667-0.1331705129-0.3370786517
2.9833333333-0.1457013039-0.3351955307
3-0.1589649822-0.3333333333
3.0166666667-0.1730619602-0.3314917127
3.0333333333-0.1881102912-0.3296703297
3.05-0.204249874-0.3278688525
3.0666666667-0.2216479137-0.3260869565
3.0833333333-0.2405060988-0.3243243243
3.1-0.2610701604-0.3225806452
3.1166666667-0.28364279-0.320855615
3.1333333333-0.3086013831-0.3191489362
3.15-0.3364228486-0.3174603175
3.1666666667-0.3677190053-0.3157894737
3.1833333333-0.4032882408-0.3141361257
3.2-0.4441928745-0.3125
3.2166666667-0.491878499-0.310880829
3.2333333333-0.5483645203-0.3092783505
3.25-0.6165609286-0.3076923077
3.2666666667-0.7008209817-0.306122449
3.2833333333-0.8079638324-0.3045685279
3.3-0.9493102784-0.303030303
3.3166666667-1.1451342349-0.3015075377
3.3333333333-1.4356988567-0.3
3.35-1.9139588878-0.2985074627
3.3666666667-2.8536879001-0.297029703
3.3833333333-5.5654536513-0.2955665025
3.4-104.6152498513-0.2941176471
3.41666666676.2250904836-0.2926829268
3.43333333333.015273296-0.2912621359
3.451.9832478207-0.2898550725
3.46666666671.4723184823-0.2884615385
3.48333333331.1662106457-0.2870813397
3.50.9614884436-0.2857142857
3.51666666670.8142959204-0.2843601896
3.53333333330.7028556659-0.2830188679
3.550.615125446-0.2816901408
3.56666666670.5439026684-0.2803738318
3.58333333330.4846127998-0.2790697674
3.60.4342087173-0.2777777778
3.61666666670.3905801924-0.2764976959
3.63333333330.3522174-0.2752293578
3.650.3180094505-0.2739726027
3.66666666670.2871186485-0.2727272727
3.68333333330.2588991775-0.2714932127
3.70.2328428579-0.2702702703
3.71666666670.2085419544-0.269058296
3.73333333330.1856630185-0.2678571429
3.750.1639280464-0.2666666667
3.76666666670.1431005785-0.2654867257
3.78333333330.1229751842-0.2643171806
3.80.1033692821-0.2631578947
3.81666666670.0841165652-0.2620087336
3.83333333330.0650615038-0.2608695652
3.850.0460545246-0.2597402597
3.86666666670.0269475421-0.2586206897
3.88333333330.0075895534-0.2575107296
3.9-0.012177988-0.2564102564
3.9166666667-0.0325263304-0.2553191489
3.9333333333-0.0536454897-0.2542372881
3.95-0.0757517154-0.253164557
3.9666666667-0.0990970293-0.2521008403
3.9833333333-0.1239818124-0.2510460251
4-0.1507718865-0.25
4.0166666667-0.1799223136-0.2489626556
4.0333333333-0.2120114289-0.2479338843
4.05-0.247790843-0.2469135802
4.0666666667-0.2882610989-0.2459016393
4.0833333333-0.334789973-0.2448979592
4.1-0.3893045768-0.243902439
4.1166666667-0.4546174229-0.2429149798
4.1333333333-0.5350100305-0.2419354839
4.15-0.6373476596-0.2409638554
4.1666666667-0.7733903359-0.24
4.1833333333-0.9651247569-0.2390438247
4.2-1.2590081771-0.2380952381
4.2166666667-1.7732153346-0.2371541502
4.2333333333-2.9232309828-0.2362204724
4.25-7.9435715613-0.2352941176
4.266666666711.4481627016-0.234375
4.28333333333.3293216858-0.233463035
4.31.9377234227-0.2325581395
4.31666666671.355423696-0.2316602317
4.33333333331.0315500709-0.2307692308
4.350.822432438-0.2298850575
4.36666666670.6739879792-0.2290076336
4.38333333330.5612644381-0.2281368821
4.40.4711101713-0.2272727273
4.41666666670.395890338-0.2264150943
4.43333333330.3308207878-0.2255639098
4.450.2726989246-0.2247191011
4.46666666670.2192417403-0.223880597
4.48333333330.1687115085-0.2230483271
4.50.119685716-0.2222222222
4.51666666670.0709002851-0.221402214
4.53333333330.0211265587-0.2205882353
4.55-0.0309445616-0.2197802198
4.5666666667-0.0868354533-0.2189781022
4.5833333333-0.1484622689-0.2181818182
4.6-0.2184134372-0.2173913043
4.6166666667-0.3004226809-0.2166064982
4.6333333333-0.4002426538-0.2158273381
4.65-0.5274062017-0.2150537634
4.6666666667-0.6991696966-0.2142857143
4.6833333333-0.9506478117-0.2135231317
4.7-1.3665563826-0.2127659574
4.7166666667-2.218073943-0.2120141343
4.7333333333-5.1120068213-0.2112676056
4.7522.3577760414-0.2105263158
4.76666666673.5675159527-0.2097902098
4.78333333331.9135910004-0.2090592334
4.81.2698426961-0.2083333333
4.81666666670.907263944-0.2076124567
4.83333333330.6565790898-0.2068965517
4.850.4547730813-0.206185567
4.86666666670.2690642735-0.2054794521
4.88333333330.074492191-0.204778157
4.9-0.1587195034-0.2040816327
4.9166666667-0.483895687-0.2033898305
4.9333333333-1.0356358296-0.2027027027
4.95-2.3374610599-0.202020202
4.9666666667-10.863594363-0.2013422819
4.98333333336.7775382702-0.2006688963
2.6832815731.040440093-0.3726779962
2.69222584490.9643120781-0.3714398634
2.70117011680.8977397742-0.37020993
2.71011438870.8389816225-0.3689881151
2.71905866060.7866938598-0.3677743384
2.72800293250.7398230251-0.3665685209
2.73694720450.6975315331-0.3653705846
2.74589147640.6591450257-0.3641804524
2.75483574830.6241144128-0.3629980483
2.76378002020.5919880328-0.3618232973
2.77272429210.5623909194-0.3606561254
2.7816685640.5350091446-0.3594964594
2.79061283590.5095778446-0.3583442272
2.79955710780.4858719552-0.3571993574
2.80850137970.4636989691-0.3560617799
2.81744565160.4428932155-0.354931425
2.82638992360.423311304-0.3538082243
2.83533419550.4048284631-0.35269211
2.84427846740.3873355758-0.3515830153
2.85322273930.3707367618-0.3504808742
2.86216701120.3549473918-0.3493856215
2.87111128310.3398924466-0.3482971928
2.8800555550.3255051529-0.3472155245
2.88899982690.3117258423-0.3461405538
2.89794409880.298500992-0.3450722187
2.90688837070.2857824145-0.3440104581
2.91583264270.2735265693-0.3429552113
2.92477691460.2616939753-0.3419064186
2.93372118650.2502487076-0.340864021
2.94266545840.239157964-0.3398279601
2.95160973030.2283916902-0.3387981784
2.96055400220.2179222544-0.337774619
2.96949827410.2077241632-0.3367572255
2.9784425460.1977738131-0.3357459426
2.98738681790.1880492717-0.3347407152
2.99633108980.1785300841-0.3337414892
3.00527536180.1691971019-0.3327482109
3.01421963370.1600323292-0.3317608275
3.02316390560.151018786-0.3307792866
3.03210817750.1421403838-0.3298035365
3.04105244940.1333818136-0.3288335261
3.04999672130.1247284429-0.3278692049
3.05894099320.1161662217-0.326910523
3.06788526510.1076815948-0.3259574311
3.0768295370.09926142-0.3250098805
3.08577380890.0908928914-0.3240678228
3.09471808090.0825634655-0.3231312106
3.10366235280.074260791-0.3221999968
3.11260662470.0659726397-0.3212741347
3.12155089660.0576868394-0.3203535784
3.13049516850.0493912059-0.3194382825
3.13943944040.0410734761-0.3185282019
3.14838371230.0327212382-0.3176232923
3.15732798420.0243218604-0.3167235096
3.16627225610.0158624173-0.3158288104
3.1752165280.0073296107-0.3149391518
3.1841608-0.0012903134-0.3140544912
3.1931050719-0.0100116543-0.3131747868
3.2020493438-0.0188493545-0.3122999969
3.2109936157-0.0278191055-0.3114300804
3.2199378876-0.0369374655-0.3105649969
3.2288821595-0.0462219892-0.309704706
3.2378264314-0.0556913731-0.3088491682
3.2467707033-0.0653656188-0.307998344
3.2557149752-0.0752662177-0.3071521947
3.2646592471-0.0854163602-0.3063106818
3.2736035191-0.0958411753-0.3054737674
3.282547791-0.1065680054-0.3046414138
3.2914920629-0.1176267235-0.3038135839
3.3004363348-0.1290501001-0.3029902409
3.3093806067-0.1408742317-0.3021713483
3.3183248786-0.1531390417-0.3013568703
3.3272691505-0.16588887-0.3005467712
3.3362134224-0.1791731704-0.2997410158
3.3451576943-0.1930473398-0.2989395692
3.3541019662-0.2075737097-0.298142397
3.3630462382-0.2228227388-0.2973494651
3.3719905101-0.2388744571-0.2965607397
3.380934782-0.2558202238-0.2957761875
3.3898790539-0.2737648854-0.2949957754
3.3988233258-0.2928294416-0.2942194707
3.4077675977-0.3131543665-0.2934472411
3.4167118696-0.3349037816-0.2926790546
3.4256561415-0.3582707453-0.2919148796
3.4346004134-0.3834840273-0.2911546846
3.4435446853-0.4108168761-0.2903984386
3.4524889573-0.4405984999-0.2896461111
3.4614332292-0.4732292964-0.2888976715
3.4703775011-0.5092013404-0.2881530899
3.479321773-0.5491263778-0.2874123364
3.4882660449-0.593774744-0.2866753817
3.4972103168-0.6441305285-0.2859421966
3.5061545887-0.7014714887-0.2852127522
3.5150988606-0.7674877167-0.28448702
3.5240431325-0.8444629142-0.2837649718
3.5329874044-0.9355605283-0.2830465794
3.5419316764-1.0452930709-0.2823318153
3.5508759483-1.1803277876-0.2816206521
3.5598202202-1.3509480584-0.2809130625
3.5687644921-1.5738909016-0.2802090197
3.577708764-1.8783537619-0.2795084972
3.5866530359-2.3202450678-0.2788114685
3.5955973078-3.0217926329-0.2781179076
3.6045415797-4.3113475235-0.2774277888
3.6134858516-7.4746342457-0.2767410863
3.6224301235-27.6272676698-0.276057775
3.631374395516.3725509009-0.2753778297
3.64031866746.3172766097-0.2747012257
3.64926293933.9104227627-0.2740279384
3.65820721122.8276534424-0.2733579435
3.66715148312.2106213954-0.2726912168
3.6760957551.8110156723-0.2720277345
3.68504002691.5303742118-0.271367473
3.69398429881.3218623679-0.2707104089
3.70292857071.1603545829-0.270056519
3.71187284261.0311603514-0.2694057804
3.72081711460.9251147958-0.2687581704
3.72976138650.8362024279-0.2681136664
3.73870565840.7603099029-0.2674722461
3.74764993030.6945278633-0.2668338875
3.75659420220.6367391115-0.2661985687
3.76553847410.5853648588-0.2655662681
3.7744827460.5392024983-0.2649369642
3.78342701790.4973185548-0.2643106356
3.79237128980.4589760696-0.2636872615
3.80131556170.4235841348-0.2630668209
3.81025983370.3906620522-0.2624492931
3.81920410560.3598133755-0.2618346578
3.82814837750.3307067678-0.2612228946
3.83709264940.3030616456-0.2606139834
3.84603692130.2766372338-0.2600079044
3.85498119320.2512240866-0.2594046378
3.86392546510.2266374071-0.2588041641
3.8728697370.2027116887-0.2582064639
3.88181400890.1792963308-0.2576115181
3.89075828080.156251968-0.2570193078
3.89970255280.1334473127-0.2564298139
3.90864682470.110756355-0.255843018
3.91759109660.0880557871-0.2552589015
3.92653536850.0652225406-0.2546774462
3.93547964040.042131329-0.2540986338
3.94442391230.0186520905-0.2535224464
3.9533681842-0.0053527832-0.2529488662
3.9623124561-0.0300315618-0.2523778756
3.971256728-0.0555467951-0.2518094569
3.9802009999-0.0820796345-0.251243593
3.9891452719-0.1098351216-0.2506802665
3.9980895438-0.1390487968-0.2501194606
4.0070338157-0.169995116-0.2495611582
4.0159780876-0.2029983614-0.2490053427
4.0249223595-0.2384470278-0.2484519975
4.0338666314-0.2768131216-0.2479011062
4.0428109033-0.3186785178-0.2473526524
4.0517551752-0.3647716478-0.24680662
4.0606994471-0.4160196427-0.2462629931
4.069643719-0.4736241691-0.2457217558
4.078587991-0.53917462-0.2451828923
4.0875322629-0.6148221304-0.244646387
4.0964765348-0.7035563918-0.2441122246
4.1054208067-0.8096639673-0.2435803897
4.1143650786-0.9395241232-0.2430508671
4.1233093505-1.1030729365-0.2425236418
4.1322536224-1.3166971924-0.2419986989
4.1411978943-1.6095042237-0.2414760235
4.1501421662-2.0386721353-0.240955601
4.1590864381-2.7341064607-0.2404374169
4.1680307101-4.0681491473-0.2399214568
4.176974982-7.7164625343-0.2394077064
4.1859192539-62.3589180199-0.2388961514
4.194863525810.4267217075-0.238386778
4.20380779774.8233736549-0.2378795721
4.21275206963.1309803426-0.2373745199
4.22169634152.3071502405-0.2368716078
4.23064061341.8147423623-0.2363708221
4.23958488531.4833148004-0.2358721495
4.24852915721.2417286192-0.2353755766
4.25747342921.0549326726-0.2348810901
4.26641770110.9035636226-0.2343886769
4.2753619730.7759547089-0.233898324
4.28430624490.6645500877-0.2334100185
4.29325051680.564119848-0.2329237477
4.30219478870.4707896679-0.2324394987
4.31113906060.3814654251-0.2319572591
4.32008333250.2934545561-0.2314770163
4.32902760440.2041787168-0.230998758
4.33797187630.1109102385-0.2305224719
4.34691614830.0104739477-0.2300481458
4.3558604202-0.1011581925-0.2295757677
4.3648046921-0.2294987259-0.2291053256
4.373748964-0.3826340845-0.2286368075
4.3826932359-0.5732761011-0.2281702018
4.3916375078-0.8229990151-0.2277054967
4.4005817797-1.1720259568-0.2272426806
4.4095260516-1.705481714-0.2267817421
4.4184703235-2.6411234758-0.2263226698
4.4274145954-4.7542047321-0.2258654523
4.4363588674-14.3444283067-0.2254100784
4.445303139319.7179203769-0.224956537
4.45424741126.4140073098-0.224504817
4.46319168314.0112616691-0.2240549076
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
r
tg(Ka)/K, -1/k
00000
00000
0
r
U(r)
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0.02-17.1891547722-0.4899105382-0.003448628-3.4381676891-0.0045373266-0.0004219075-0.0004209799-0.0004209188-0.0004209183
0.04-34.3778886261-3.4141320941-0.0910116489-6.8759144599-0.0331410472-0.000452492-0.0037672179-0.0004560187-0.0004209706
0.06-51.5666224801-9.5794099843-0.6125150489-10.3136612307-0.1096875089-0.0006596497-0.1242992745-0.0021598119-0.0004253752
0.08-68.755356334-18.5609274263-2.1840491427-13.7514080014-0.2556747206-0.0014208503-0.7357541226-0.0145974623-0.0004787589
0.1-85.9440901879-29.6341577139-5.4064123959-17.1891547722-0.4899105382-0.003448628-2.1024204332-0.055815898-0.0007565635
0.12-103.1328240418-42.1874281409-10.588019662-20.626901543-0.8280251885-0.00788242-4.1930236149-0.1483551027-0.0016818378
0.14-120.3215578958-55.7849029576-17.7061134893-24.0646483138-1.2822425833-0.0163636189-6.8423509522-0.3151171307-0.0040402926
0.16-137.5102917497-70.1301566977-26.5367983284-27.5023950846-1.8613892603-0.0310901038-9.8826499539-0.5769031992-0.0090816784
0.18-154.6990256036-85.0221624333-36.7920054185-30.9401418554-2.5710955621-0.0548470525-13.1847510071-0.9511073729-0.0186012842
0.2-171.8877594575-100.3227082805-48.1976919316-34.3778886261-3.4141320941-0.0910116489-16.6585128678-1.4511496458-0.0349970971
0.22-189.0764933115-115.9348920792-60.5227096949-37.8156353969-4.3908242143-0.1435304083-20.2433040179-2.0864027324-0.0612991958
0.24-206.2652271654-131.7893381622-73.5822895513-41.2533821677-5.4994949133-0.2168692094-23.898800302-2.8624466224-0.1011690742
0.26-223.4539610193-147.8353556104-87.2320280523-44.6911289385-6.7368980634-0.3159376775-27.5981929163-3.7815220479-0.158867947
0.28-240.6426948732-164.035192627-101.359816408-48.1288757093-8.0986164374-0.4459911624-31.3235896224-4.8430807968-0.2391946856
0.3-257.8314287272-180.3602364363-115.878471259-51.5666224801-9.5794099843-0.6125150489-35.0630067637-6.0443618728-0.3473961053
0.32-275.0201625811-196.7884515131-130.7197839201-55.0043692509-11.1735085788-0.8210973368-38.8083876922-7.3809317507-0.4890534189
0.34-292.208896435-213.3026194466-145.8299537209-58.4421160216-12.8748496118-1.0772961904-42.5543251389-8.847171292-0.6699514059
0.36-309.3976302889-229.8891073013-161.1661575519-61.8798627924-14.6772646307-1.3865093729-46.297206341-10.4366834614-0.8959367966
0.38-326.5863641429-246.5369908308-176.6939908618-65.3176095632-16.5746212675-1.7538521232-50.0346476152-12.1426260746-1.1727739821
6.2832
57.2957795131
3.1415926536
2
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
l=0
1
2
0
1
2
a=3 fm
a=5 fm
k (fm-1)
delta (degres)
a=3
k0^2Resonances
100001.85302213693.49381077914.8138334163
1500002.68453231684.2629792587
2000001.48550118143.6294616901
25000002.8588445498
Etats lies
101.51789327692.56144490473.0357865538
151.006975672.63362867543.36949551123.7567938458
202.32551069663.44354468534.0696437194.3826932359
251.38333333333.154.054.64.9166666667
dphasage sphre dure
l=0
l=2
l=1
k
delta
dephasages aphere dure avec et sans coulomb
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
181.4677250619177.960772046359.02533361160.12114629372.4206818193
182.991425716176.0282823554358.0876004190.29360993714.9632137118
184.6306289674174.2960852553357.22158805350.5683467327.7610646265
186.4525440843172.8352836479356.45815331930.995906597510.9732459508
188.5374794108171.6911653169355.82306040061.62699680614.803215047
190.9865344084170.8852625167355.33655164622.513910570219.5257951172
193.933041482170.4207956333355.01360666973.713075506725.5236760624
197.5599224122170.2892464653354.86473906475.289042210633.32465615
202.1256891894170.476463032354.89713878587.320406147943.5895168752
208.0004563179170.9675542999355.11598401839.908468574156.89243193
215.7028631155171.7504870203355.525797365713.189895795173.0631620291
225.8869661673172.8186568489356.131785388817.355080585590.4563910372
239.1186845724174.1728456433356.941163562122.6735751056106.6096691023
255.2095654332175.8230047822357.964525671829.5238994535120.0359917726
272.4858795976177.7903068106359.217370661938.4078834087130.6853035126
288.4698226076180.1099415492360.721960052749.878600718139.1631493861
301.6819764517182.8352362061362.509759566664.2250973797146.1220119282
312.0823312095186.0438806373364.62483981680.847666834152.0756726533
320.2777735488189.8473471048367.128800979197.9660400241157.3980609907
326.9158843901194.4049217817370.1080801075113.5983061791162.3629802757
332.5024970526199.9436452137373.6849189144126.8145868649167.1816713603
337.4015061311206.7831086446378.0337289045137.7481017598172.0315921239
341.8741995566215.353796351383.4045311164146.9565142561177.0786933062
346.115709766226.165639965390.1522895111155.0136829707182.4966413043
350.2820850724239.6174556492398.757705339162.3927105605188.4859353816
354.5101233997255.5272763612409.7824638596169.4720561214195.2947146756
358.9331797519272.6555961753423.6163452932176.5717622283203.2399147979
363.695762642289.1030748364439.8901171024183.9909084841212.7179028552
368.9693142959303.5250010401457.0146962842192.0406255251224.1688655506
374.9711159554315.6593489961472.9091534118201.0702715093237.9165334555
381.9867657431325.9007944155486.3815094536211.4762258994253.8139692577
390.3909446006334.8066820812497.4002608639223.661452185270.8970682855
400.6429935255342.8840425261506.480233649237.8852090546287.6375543062
413.1907110947350.5536027779514.2001516944253.9711449051302.8270562582
428.1707124938358.1743693809521.0406591276271.0659229182316.0984259068
444.935082861366.0802990503527.3753115006287.8815686217327.7089975665
461.9554239484374.6149806696533.5026783152303.3933314816338.1467805602
477.6398889859384.1579075212539.6819518571317.2621380647347.9144943179
491.2344717922395.1271708682546.1648524118329.6939210273357.4712301529
502.8302630771407.9191162319553.224895519341.1297310249367.2419298069
512.8970769281422.7210817812561.1849298501352.0553796808377.6423163235
521.9574430472439.1997558214570.4373003662362.9383953973389.0910372838
530.4772889939456.3425709643581.4320984524374.224028749401.978758649
538.863000318472.8579906068594.5702372959386.3386731079416.5516346866
547.4913070621487.8804222189609.913481299399.6627279175432.6955675119
556.7429696699501.2382426723626.7854968522414.4368554701449.7601846532
567.026128021513.2239187777643.7695348378430.5944378748466.7183414728
578.7673876552524.300658851659.4627504664447.6243603542482.6773520086
592.3246175693534.9502566349673.2197351418464.6806238853497.2617905877
607.7669889165545.6325526936685.1372181285480.9746735794510.5818335586
20
15
25
10
12
k
delta
dephasages puits carre a=3
0.1110
0-0.0573229-0.301641.23654
10.04234575250.48375816342.7076676743
20.09230414820.94740577244.0810684412200.3020528363.020920384218.0097770801
30.12562514411.26915632685.3604079736400.37013287943.70142927124.5466903631
40.15061993771.51413498996.5506979232600.41026556084.102700595928.5053372832
50.17061727171.71153054987.657846641800.43882642754.388289651531.341863163
60.18728239541.87667922728.68822346761000.46101624224.610178673533.5516976078
70.2015671382.01857628189.648293831200.47916531414.791664420735.3616076395
80.2140664872.142931276310.54434921451400.49452100884.945218362736.8941531008
90.22517714092.253588497511.38233043961600.50782960295.078302350338.2230449592
100.23517680762.3532571512.16772860291800.51957325125.195737492639.3960584233
110.24426746632.443917037212.90554366312000.53008157295.300819749540.4459226532
120.25260060672.527058269113.60028193932200.5395898995.395902300241.3960383408
130.26029276272.603830160414.25597756552400.54827212435.482724011942.263715119
140.26743549832.675137625114.87622705152600.55626039045.562606251743.0621167116
150.27410206622.741705788915.4642296552800.5636574685.636576693343.8014870355
160.28035198492.804124598916.02282897043000.57054486385.705450381544.4899542562
170.286234272.862880421616.55455303763200.57698831025.76988462545.1340758979
180.29178976842.918378926917.0616515423400.58304159045.83041724345.7392190226
190.29705287772.970961988517.54612947113600.58874926945.887493880246.3098319441
200.3020528363.020920384218.00977708013800.59414868815.941487936746.8496426062
210.30681470483.068503487518.454196294000.59927144415.992715385847.36180616
220.3113601283.113926766918.88082378314200.60414451296.041445978147.8490165919
230.31570792673.157377662319.29095112364400.60879110736.087911839548.3135924213
240.31987456923.199020241419.68574224334600.61323134646.132314158648.7575433756
250.32387454793.238998928520.06624862054800.6174827826.174828451249.1826228949
260.32772068283.277441518520.43342245435000.62156081766.215608750949.5903699317
270.33142436963.314461634420.78812810635200.62547904526.254790977549.9821425628
280.3349957833.350160747121.13115204675400.6292495196.292495670750.359145266
290.33844404513.384629848121.46321151425600.63288297856.328830226150.7224512409
300.34177736613.41795084421.78496206865800.63638903346.363890739851.0730208181
310.34500316143.450197726422.09700419026000.63977631666.397763539751.41171675
320.34812815123.481437559822.39988905866200.64305261216.430526466251.7393169981
330.3511584453.511731319822.69412362376400.64622496316.462249949652.0565254909
340.3540996133.54113460822.98017506546600.64929976276.49299792252.363981229
350.35695674813.569698265823.25847472446800.6522828326.522828592452.6622660318
360.35973451873.597468902423.52942157487000.65517948586.551795110852.9519111624
370.36243721483.624489351623.79338529847200.65799459036.579946137253.2334030201
380.36506878773.650799068824.05070901337400.66073261176.607326334153.5071880535
390.36763288463.676434477424.30171177600.66339765916.633976792453.7736770191
400.37013287943.70142927124.54669036317800.66599352156.659935402454.0332486874
410.3725718993.725814680224.78592196318000.66852370046.68523717854.2862530795
420.37495284693.749619706325.0196651448200.67099143796
![ESTRUCTURA NUCLEAR · 2018-05-29 · [Joa] "Quantum Collision Theory", C.J. Joachain, North Holland, 1983 [F&L] "Theory of Nuclear Reactions", P. Frobrich y R. Lipperheide (Oxford](https://static.fdocument.pub/doc/165x107/5eb8d82cf7230f50af77d3a4/estructura-nuclear-2018-05-29-joa-quantum-collision-theory-cj.jpg)
