Description of the Adiabatic Coupled-Channels Born Approximation
(ACCBA) program for analysis of the (d,2He) reaction.
* The name of ACCBA was introduced by the late Prof. Tamura (Texas A&M)
Details of calculation is given in
[1] H. Okamura, Phys. Rev. C 60 (1999) 064602.
A longer writeup is given under directory doc/, which is unfortunately
written in Japanese.
See also references:
[2] H. Okamura et al., Nucl. Instr. and Meth. A 406 (1998) 78.
[3] H. Okamura et al., Phys. Lett. B 345 (1995) 1.
In the following, all numeric values are given in free format.
Note that / (slash) terminates the input for the line thus setting
remaing parameters, if exist, to be zero.
The distance between the target and the c.m. of p-p system is refered to
as RL (radius larger), while the relative coordinate between p-p (or p-n)
is refered to as rs (radius smaller).
Line 1: title
title (A) any string less than 80 characters
Line 2: DWBA, point-proj, triple.c.s.
DWBA = T treat 2He as a particle (but with finite size),
assuming the optical potential acts on the
center of mass of p-p system.
= F generate the final scattering wave from proton-B
optical potential by solving adiabatic coupled-
channels equation.
point-proj. = T two-body calculation, treating 2He as a point
particle, just to compare with ordinary two-body
DWBA code.
= F three-body calculation.
triple.c.s. = T output triple-differential cross section
to unit 1
= F do not output
Line 3: thmin, thmax, dth
thmin minimum of angular distribution (deg)
thmax maximum of angular distribution (deg)
dth step of angular distribution (deg)
Line 4: A, ZA, IA, IB, Elab, Qval, Ex
A mass of target (in unit of *nucleon* mass = (mp+mn)/2,
not in mass unit = 931.494 MeV)
ZA charge of target
IA spin of target (real number, so 1.5 for 3/2)
IB spin of residual
Elab beam energy (MeV)
Qval reaction Q value (MeV)
Ex excitation energy (MeV)
Line 5: ptr, ntr, (jtr(i),i=1,ntr)
ptr parity transfer (either +1 or -1)
ntr number of j-transfer (j is total angular momentum)
jtr(i) i-th j-transfer, where i=1..ntr
Line 6: nRL, dRL, Lmax
nRL number of division for RL (must be even)
dRL division of RL (fm)
N.B. RL is divided in equal step
Lmax maximum number of partial wave expansion
Line 7: nrs, drs, mrs, lamax, lbmax
nrs number of division for rs (must be even)
which is used in integration of T-matrix
drs division of rs (fm)
nrs*drs gives maximum radius of integration
mrs number of division for drs interpolation
nrs*mrs is the division number used for solving
p-p scattering wave function.
Since T-matrix depends on rs rather moderately
if p-p relative energy is not large, nrs does not
need to be large, which saves calculation time
considerably, but smaller division is needed
in calculation of p-p wave function, resulting in
introduction of parameter mrs.
lamax = 0 do not include D-wave of deuteron
2 include D-wave of deuteron
lbmax = 0 do not include D-wave of p-p system
2 include D-wave of p-p system,
which requires to solve coupled-channels
equation, increasing CPU time considerably.
lamax and lbmax must be either 0 or 2.
In ordinary situations, both D-wave contributions
are negligibly small (Ref. [1]).
Line 8: nE12, E12min, E12max
nE12 division of p-p relative energy
E12min integration minimum of p-p relative energy
E12max integration maximum of p-p relative energy
Integration over E12 is carried out by Gauss-Legendre
method, not in equal step. The dependence of T-matrix
on E12 is moderate, so nE12 does not need to be very large.
For discussion on the choice of E12{min,max},
see refs. [1] and [2].
[Following two lines are deuteron optical potential parameters.
See Ref. [1] for definition. ]
Line 9: VR, rR, aR, WV, WD, rI, aI, rC
VR depth of real potential (MeV)
rR reduced radius of real potential (fm)
aR diffuseness of real potential (fm)
WV depth of volume imaginary potential (MeV)
WD depth of surface imaginary potential (MeV)
rI reduced radius of imaginary potential (fm)
aI diffuseness of imaginary potential (fm)
rC reduced radius of charge distribution (fm)
Line A: VLS, rLS, aLS
VLS depth of spin-orbit potential (MeV)
rLS reduced radius of spin-orbit potential (fm)
aLS diffuseness of spin-orbit potential (fm)
[If DWBA=T in Line 2, the optical potential parameters for 2He follow
in 2 lines, otherwise, the proton optical potential *without* spin-orbit
part must be given in *a* line. The spin-orbit potential can not be
included in adiabatic coupled-channels calculations. ]
Line B: VR, rR, aR, WV, WD, rI, aI, rC
[Parameters describing two-body effective interaction follow,
which may appear several times to be superimposed]
Line C: s t x r n (V(i),mu(i),i=1,n)
s spin transfer (either 0 or 1)
(total angular momentum transfer for projectile)
N.B. s=-1 terminates the input of effective interaction
and proceed to next section
t isospin transfer (either 0 or 1)
x = 1 Yukawa-type central interaction
= 2 Delta -type central interaction
(used to include knock-on exchange contribution)
= 3 r^2*Yukawa-type tensor interaction
r = 1 real part
= 2 imaginary part
n number of ranges
V(i) magnitude of interaction (MeV) , i=1..n
mu(i) range of interaction (fm^-1), i=1..n
[Single-particle wave functions are generated by using following
potential geometry parameter. ]
Line D: r0, a, VLS, r0C
r0 reduced radius of single-particle potential (fm)
a diffuseness of single-particle potential (fm)
VLS depth of spin-orbit part of .... (MeV)
r0C reduced radius of charge distribution (fm)
[Each single-particle wave function is generated either by giving
the depth of potential or the binding energy, as well as (n,l,j)]
Line E: orbit, VorE, V0, BE
orbit string specifying the orbit, which consists of
particle (proton or neutron), node number (n), orbital
angular momentum (l), and total angular momentum (j)
expressed in fraction, in this order.
For example, 'n0p3/2' stands for n=0, l=1, and j=3/2
orbit for neutron.
N.B. 'end' terminates the input of single-particle
wave function and proceed to the next section.
VorE = 'V' wave function is generated by using V0, and
search the binding energy taking BE as initial
value.
= 'E' wave function is generated by using BE, and
search the potential depth taking V0 as initial
value.
N.B. strings are not necessarily enclosed by quotation
for Linux (f2c+gcc) and Solaris, but must be enclosed
for Digital UNIX and VMS DEC-Fortran.
V0 potential depth (MeV)
BE binding energy (MeV)
Initial parameters V0 or BE must be properly given
for successful search.
[Spectroscopic amplitudes describing the transition of target side
must be given for each jtr(i), where i=1..ntr as given in Line 2. ]
Line F: orbit1, orbit2, amp
orbit1 string specifying the hole orbit
N.B. 'end' terminates the input of amplitude for this
jtr(i) value, and proceed to the next section.
orbit2 string specifying the particle orbit
amp spectroscopic amplitude
Some conventions of single-particle wave function (spwf) are:
* node number does not include the one at origin and infity.
* radial part of spwf is positive near the origin
* angular part of spwf include i^l
* coupling order is j = l + s
which are the same as those of TWOFNR by Igarashi.
DISCLAIMER:
* Only the non-relativistic kinematics is provided.
As wave functions are treated essentially in non-relativistic way,
contradiction with the relativistic three-body kinematics appears
in enhanced form, sometimes.
* Recoil correction of shell model description must be taken into
account outside of the program, like in ordinary DWBA programs.