Radial coordinates:
hcm, rmatch, rintp, hnl, rnl, centre, hnn, rnn, rmin, rsp, cutl, cutr, cutc,
rasym, accrcy, switch, sinjmax, ajswtch,
Partial waves: jtmin, jtmax, absend, jleast, jump, jbord, pset, jset, iso, llmax,
Angular distributions: kqmax, thmin, thmax, thinc, pp, koords, nearfa, dist0,
Defining coupled equations:
inh, nnu, maxl, minl, mtmin, epc, erange, dk, plane, elpmax, rela, relref,
ccbins, complexbins, sumform, ompform, pluto, unitmass, finec,
Incident channel: pel, exl, lab, lin, lex, elab, nlab,
Solving equations:
ips, it0, iter, fatal, iblock, pade, nosol, dry, smallchan, smallcoup, ccreal,
psiren, initwf, mpihelp, maxcoup, expand,
R-matrix setup:
nrbases, nlagcc, nrbmin, pralpha, pcon, rmatr, btype, bndx, buttle, weak,
krm, eigens, meigs, vsearch, echan, enodes, nparameters, eobs
Trace variables: chans, listcc, treneg, cdetr, smats,
Output details:
xstabl, nlpl, waves, lampl, veff, kfus, nfus, wdisk, bpm, melfil, cdcc, tcfile, tcfilename,
dist0, tmp, grace, boldplot
Wave functions calculated at intervals of HCM up to abs(RMATCH).
If RMATCH 0, then use values of RASYM, ACCRCY, SWITCH, AJSWITCH for coupled Coulomb wave functions.
Non-local kernels calculated at intervals of RINTP, and for a non-local () range of RNL centred at CENTRE in steps of HNL.
RMATCH and RINTP are rounded to multiples of HCM, and HNL is rounded either to a multiple or a sub-multiple of HCM.
For two-nucleon transfers, the nucleon-nucleon distance is discretized from RMIN to RNN in a multiple of 6 Gaussian quadrature points to give step size close to HNN.
RSP is the upper limit of state radius when folding single-particle states (bound states or continuum bins) with KIND=3 or 4 couplings.
CUTL: set the number of radial points per of the lower radial cutoff when integrating the radial equations. Default = –1.6
When CUTL0, use (total angular momentum of CC set),
When CUTL0, use (orbital angular momentum of incoming partial wave).
Using CUTL0 gives more accurate analyzing powers.
CUTR = lower radial cutoff (fm). Combining with CUTL is to use = max(CUTL**HCM,CUTR).
If CUTR 0, put cutoff at point-Coulomb turning point CUTR.
CUTC = lower radial cutoff (in fm) for off-diagonal couplings.
Use coupled Coulomb wave functions from CRCWFN out to asymptotic radius RASYM from
inner radius abs(RMATCH) for those partitions in which PWF is TRUE.
If RASYM 0, then determine the outer radius in order that classical
Coulomb trajectories reach an angle abs(RASYM) degrees.
ACCRCY is an accuracy parameter controlling the piecewise step length. Default is 0.01: smaller values give greater accuracy.
SWITCH is the radius at which to switch from Airy functions to sines and cosines in piecewise method. Default is 1000 fm. If SINJMAX, then change switchover condition to SINJMAX.
AJSWITCH Normally the Coupled Coulomb wfns are matched to zero and the Numerov integration is omitted when the Coulomb distance of closest approach is more than 4.5 fm outside abs(RMATCH) (or the –CUTR distance if CUTR negative). This is only allowed when AJSWITCH. Default is 0.0
JSET = number of CRC sets to calculate before stopping (0 = all sets)
Of course, the simplest and fastest way to use the isocentrifugal approximation is to put all spins and parities to , and all transition multipoles to . The ISO variable is not needed then.
Give cross sections (and tensor analyzing powers up to rank K = KQMAX)
for centre-of-mass scattering angle from THMIN
to abs(THMAX) in steps of THINC.
Elastic channels normally output the ratio to Rutherford, unless THMAX .
NNU is the number of Gaussian integration points in the angular integration used for the non-local transfer kernels. NNU should be a multiple of 6; NNU = 18 is the minimum, and 24 or 36 give acceptable accuracy for all the reactions tried so far.
MAXL,MINL are the maximum and minimum values for the non-local kernels. If zero, MAXL has the default value JTMAX+6, and if MINL 0 it takes the default value JTMIN-6.
MTMIN is the lowest L-transfer for calculating transfer form factors using the m-dependent expressions for spherical harmonics. Putting MTMIN = 0 gives default value MTMIN = 6 (use MTMIN 0 to avoid invoking default, if all transfers are to use this method).
EPC = percentage cutoff accuracy in the NNU angular integration. If zero, the default is (30/NNU)%.
ERANGE = range of energies of the upper and lower boundaries
of continuum bins:
if ERANGE 0, then ratio of these energies;
if ERANGE 0, then difference of the energies in MeV.
DK = step size of (fm) for integration over the ERANGE to construct the continuum bin.
ELPMAX = energy ELAB below which the LPMAX limits in each partition are applied
The defaults for PEL,EXL,LIN & LEX are all 1, and the default for LAB is PEL, so these variables can be normally omitted.
Solve the coupled channels equations by at least IT0 iterations, and up to ITER iterations. Stop sooner if the absolute differences between successive -matrix elements (scaled by (2+1)/(2.JTMAX+1)) are less than IPS percent. (Excited state pairs with IGNORE set in the &STATE namelist are not counted against IPS).
Putting IT0=ITER zero solves only the elastic channel (along with the IBLOCK channels: see below). Putting IT0=ITER = 1 or 2 etc. gives 1 or 2-step DWBA.
Normally, a run is terminated if more than ITER steps are required for
convergence.
Setting FATAL=False allows continuation even after
convergence has failed after abs(ITER) iterations.
Iterations are normally also stopped if the successive differences are smaller than the errors estimated for the numerical integration of the coupled equations. Setting IPS uses abs(IPS), without this extra check.
IBLOCK is the number of pairs of excitation levels (starting from partition 1, excitation 1) that are coupled exactly by blocking together.
PADE
= 0 for no Pade acceleration,
= 1 for Pade acceleration by the epsilon algorithm,
= 2 for Pade acceleration by finding the N/D polynomials.
SMALLCOUP: if all nonelastic channels are weaker than the fraction SMALLCOUP of unitarity, then permanently change from coupled-channels to DWBA.
CCREAL = T: assume all potentials and couplings real-valued
NRBASES = target number of radial basis states in each channel.
(Use 2*NRBASES for the elastic and first-inelastic channel for more accuracy).
If NRBASES 0, then use Lagrange mesh basis with NLAG=–NRBASES basis functions.
BUTTLE = 4 for none, 0,2 for complex, 1,3 for real
(2,3 without energy shift) Buttle correction.
(default 0)
PRALPHA = print basis-state eigenvalues to files fort.60,61,62,63
PCON = trace variable for calculation of radial basis states (same meaning as IPC for single-particle bound states).
RMATR = R-matrix matching radius (default RMATCH ). Warning: RMATR will be changed to an even multiple of HCM.
BNDX(i) is used to set the R-matrix Boundary Condition number depending on BTYPE. Use i=1,2 for positive, negative parity coupled channels sets (respectively).
Energy , where , the logarithmic derivative for all radial basis states at =RMATR, with having the same sign as EBETA(i).
BTYPE = E,k, L,B, S : methods to calculate Bloch parameter B from BNDX. If BNDX(i) is the energy for 'E' or wave number for 'k, then B is inverse logarithmic derivative of Coulomb function there. Otherwise B = –L for 'L', B = BNDX(i) for 'B', and S (shift function) for 'S'.
If WEAK0, then non-elastic columns of the R-matrix are set to zero, when penetrabilities WEAK.
Then follow NANGL print operations in FORMAT(1P,6E12.4), repeating the FORMAT for each operation if KQ1PR is large, of THETA, elastic xs (mb), , , , , , , etc.
The phase convention here is that there is no Coulomb phase shift for in the Coulomb scattering amplitude : factors such as appear in the 's.
The following data formats are used when WDISK 0 :
line A: (I4,2F8.4,F8.1,I3) NR,H,ENLAB,JTOTAL,PARITY,MP,MT,ZP,ZT : number radial points, step size, lab. energy, J,pi, projectile and target masses and charges line B: (2I4,2F6.1,I4,F6.1,2F15.10,f12.8) IT,L,J,JTOT,LIN,JIN,SMAT (complex), ETA
where
IT = index to excited state pair, counts lines 7.
L = partial wave
J = L + projectile spin
JTOT = total spin = J = J + target spin
LIN = incoming partial wave
JIN = incoming J value.
SMAT = S matrix element for this partial wave.
line C: (6E12.4) (psi(I),I=1,NR) wave function line C is repeated until NR complex values given NB: the first point psi(1) = 0 always, as at r=0
Lines B & C are repeated for each channel, until IT 0.
When WDISK 0, successive records contain the two real values of psi(I), starting IN THIS CASE, from I=2 (i.e. ).
line Y:(i2) 1 (indicating CDCC=1 format below) line Z: (A120) HEADNG from Fresco input. line A: (F10.4,3F8.4) ENLAB,Bproj,H2SM,e^2,Btarg,inp, (Qval if inp=1) lab energy,projectile binding energy, hbar^2/2.m, e^2, target binding energy,inp, Qval if inp=1 line B: (7f8.4) massp,masst,massc,massv,massr masses: projectile,target,core,valence,residual line C: (7f8.4) Zp,Zt,Zc,Zv,Zr charges line D: (7A8) namep,namet,namec,namev,namer names line E: (7f8.1) Jp,Jt,Jc,Jv,Jr g.s. spins line F: (7i8) Pp,Pt,Pc,Pv,Pr g.s. parities If inp=1, cards B-F (incl) have further #6 and #7 values for 'initial projectile' and 'initial target' too. line G: (4I4) NBINS,NKMAX,NEXB,NNJMAX no. CDCC bins, max NK, no. excited states, max(2*Jex+1) line H: (I4,2f8.4) NANGL,THMIN,THINC (cm angular range from \&FRESCO) for each of the NBINS bins: line I:(i2,2f4.1,3f8.4,2i4) l,j,Emid,kmin,kmax,NK,KN,ISC l,j: quantum numbers (s==Jv) Emid: centre of bin with respect to continuum threshold kmin,kmax,NK: Min,max and number of k values in bin integral KN: original KN index for bin state ISC: normalisation used for bin for each IK=1,NK line J: (10f8.4) delta(IK): nuclear phase shift used in bin integral (radians) for each excited state pair in the entrance partition: IA=1,NEXB:: line K: (f4.1,i4,f8.4,i4) Jex,Parity,Eex,IBIN: Jex : spin of this projectile excited state (not including core spin) Parity: parity of this projectile state Eex: excitation energy of this state above g.s. IBIN: (first) bin defined for this excited state for each IANG=1,NANGL: read complex numbers: line L: (6E12.4): ((FAM(MEX,MP,IANG,IA),MEX=1,2*Jex(IA)+1),MP=1,2*Jp+1)
The phase convention for all CDCC values is that there is no Coulomb phase shift for in the Coulomb scattering amplitude : factors such as appear in the 's.t
Summary of bin normalisation factors for different ISC values:
ISC
= 2:
= 4:
= 12:
= 14:
line Y:(i2) 2 (indicating CDCC=2 format below) line Z: (A120) HEADNG from Fresco input. line A: (F10.4,3F8.4) ENLAB,Bproj,H2SM,e^2,Btarg,inp, Qval if inp=1 lab energy,projectile binding energy, hbar^2/2.m, e^2, target binding energy,inp, Qval line B: (7f8.4) massp,masst,massc,massv,massr masses: projectile,target,core,valence,residual line C: (7f8.4) Zp,Zt,Zc,Zv,Zr charges line D: (7A8) namep,namet,namec,namev,namer names line E: (7f8.1) Jp,Jt,Jc,Jv,Jr g.s. spins line F: (7i8) Pp,Pt,Pc,Pv,Pr g.s. parities If inp=1, cards B-F (incl) have further #6 and #7 values for 'initial projectile' and 'initial target' too. line G: (5I4) NBINS,NKMAX,NEXB,NNJMAX,NCHMAX no. CDCC bins, max NK, no. excited states, max(2*Jex+1), max nch line H: (I4,2f8.4) NANGL,THMIN,THINC (cm angular range from \&FRESCO) line I: (I4) NCE (number of excited states. NCE=0 for only gs). for each of the ICE=1...NCE core excited states (card skipped if NCE=0) lines J: (I4,2f8.4) IPARCE, JCE, ECE (parity -1,+1; spin; energy of excited states) (for the gs: parity=Pc, spin=Jc, energy=0.0) for each of the NBINS bins: card K:(f4.1,2I4,f4.1,3f8.4,2i4) Jex,Pex,nch,Emid,kmin,kmax,NK,KN,ISC Jex: overall spin [ (l s)j, JCE(ICE); Jex> Pex: overall parity = parity(ICE) * (-1)**l nch: number of partial wave channels coupled to Jex/Pex. IL: incident channel (1<= IL <= nch) Emid: centre of bin with respect to continuum threshold kmin,kmax,NK: Min,max and number of k values in bin integral KN: original KN index for bin state ISC: normalisation used for bin For each partial wave c=1..nch line L: (i4,f4.1,i4) l,j,ICE: quantum numbers. Use s=Jv. for each IK=1,NK for k=kmin+(IK-1)*kinc where kinc = (kmax-kmin)/(NK-1) line M: (2f10.6) delta(IK),k: any nuclear phase shift used in bin integral (radians) line N: (10f10.6) S(:,:) the full scattering S matrix for nch channels (always nch*nch, so closed channels included) for each excited state pair in the entrance partition: IA=1,NEXB:: line K: (f4.1,i4,f8.4,i4) Jex,Parity,Eex,IBIN: Jex : spin of this projectile excited state (including core spin) Pex: parity of this projectile state Eex: excitation energy of this state above g.s. (including core energy) IBIN: (first) bin defined for this excited state for each IANG=1,NANGL: read complex numbers: line L: (6E12.4): ((FAM(MEX,MP,IANG,IA),MEX=1,2*Jex(IA)+1),MP=1,2*Jp+1)