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• This code can calculate the α+α(L=0, 2, 4), α+p, and α+n(L=0, 1),
  elastic scattering phase shifts in the RGM (Resonating Group Method)[1,2].

• The internal wave function of the α particle is approximated by the single (0s)⁴ h.o. wave function.
  ν_α (= mω/2ħ) = 0.26 fm^-2 reproduce nearly the experimental charge radius of the α particle 1.47 fm.

• The cluster relative wave function inside the channel radius is approximated
  by a superposition of the tempered Gaussian basis, see Eqs. (4) and (5) in Ref.[3],
  and is then connected with the exact Coulomb function at the channel radius.
  The microscopic R-method [4,5] is employed in order to obtain the scattering S-matrix.

• The basis set used to approximate the cluster relative w.f. are following,

     i             νi                                  bi 
  

  1.    0.6122448979591778E+01    0.4041451884327400E+00
  2.    0.3876910717810504E+01    0.5078753097033172E+00
  3.    0.2454971329932769E+01    0.6382293729798237E+00
  4.    0.1554558427952545E+01    0.8020408252808562E+00
  5.    0.9843910910293477E+00    0.1007897023626226E+01
  6.    0.6233447406503856E+00    0.1266589403200112E+01
  7.    0.3947198112999908E+00    0.1591679188144666E+01
  8.    0.2499479329369778E+00    0.2000208300789485E+01
  9.    0.1582742172826667E+00    0.2513592736744086E+01
  10.    0.1002237848582533E+00    0.3158745238542828E+01
  11.    0.6346458206376170E-01    0.3969486120866696E+01
  12.    0.4018759800604615E-01    0.4988316205906549E+01
  13.    0.2544794247400798E-01    0.6268644810043293E+01
  14.    0.1611436881753891E-01    0.7877589577812519E+01
  15.    0.1020408163264653E-01    0.9899494936614833E+01

  where the ν_i and b_i are parameters in the tempered Gaissian basis
  such as Exp[-ν_i * r²] = Exp[-( r / b_i )²] .

• As for the effective nucleon-nucleon force V_ij(r_ij),
  the Minnesota potential has a follwing form,
  
  V_ij(r_ij) = {U₁ + 1/2*(1+P^σ) U₂ + 1/2*(1-P^σ) U₃} { 1/2*u + 1/2*(2 - u P^r)} ,
  where u is the exchange mixture-parameter.
  The Volokov force has,
  V_ij(r_ij) = (U₁ + U₂) ( 1 - m + m P^r)} ,
  where m is the majorana parameter.
  The U_i ( i=1,2,3 ) is definced as
  U_i = V_i Exp[- μ_i r²] ,
  and P^σ and P^r are the Bartlett(spin exhange) and Majorana(space exchange) operator, respectively.

• The Coulomb force is included in this calculation.

• As for the spin-orbit force, the definitions of L and S are
  
  L = - (1/2) i ħ r_ij (∇_j - ∇_i)
  S = (σ_i+ σ_j)
  See Refs [6, 7].

  References

  [1]. K. Wildermuth and Y.C. Tang, A Unified Theory of the Nucleus
        (Vieweg, Braunschweig, 1977).

  [2]. K. Langanke, in Advances in Nuclear Physics, vol. {\bf 21},
        editors J.W. Negele and E. Vogt (Plenum, New York, 1994), p. 85.

  [3]. K. Arai, P. Descouvemont, D. Baye, and W. N. Catford, Phys. Rev. C 68, 014310(2003).

  [4]. D. Baye, P.-H. Heenen, and M. Libert-Heinemann, Nucl. Phys. A291, 230 (1977).

  [5]. H. Kanada, T. Kaneko, S. Saito and Y. C. Tang, Nucl. Phys. A444, 209 (1985).

  [6]. A. Csoto, Phys. Rev. C 48, 165 (1993).

  [7]. L. Reichstein and Y. C. Tang, Nucl. Phys. A158, 529 (1970).

Copyright (C) 2004 by Koji Arai .