&COUPLING namelists

Now read in namelists for each kind of coupling between partitions and/or between excited states, ending with a namelist which is empty or has ICTO=0. Note that if deformed potentials were given as channel optical potentials then there will already be some couplings between excited states.

ICTO, ICFROM

,KIND, IP1,IP2,IP3, P1,P2, , IP4,IP5

The coupling is from all the states in partition ICFROM to all the states in partition ICTO.

Couplings in the reverse direction are also included unless ICTO $<$ 0, except for KINDs 1 & 2 where finer control is allowed.

JMAX, RMX

Couplings are only active for J $<$ JMAX and Radius $<$ RMX, (if JMAX=0, use JTMAX, and if RMX=0, use RMATCH).

KIND

The couplings can be of 8 KINDs:

= 1 : general spin transfer for projectile/transfer couplings
= 2 : electromagnetic one-photon couplings
= 3 : single-particle excitation of the projectile
= 4 : single-particle excitation of the target
= 5 : zero-range or LEA transfer with strength P1 and finite range radius P2 (in fm.)
= 6 : LEA transfer using $D_0$. & $D$ from bound states
= 7 : finite-range transfer
= 8 : non-orthogonality correction to a KIND 5,6,7 transfer

After &coupling namelists for KINDs 2,3,4,5,6,7 (& 8 if IP2$>$0), spectroscopic amplitudes are read in by means of &cfp namelists. These coupling types are those for which ICTO & ICFROM are different, one being a core partition and the other a composite nucleus. One table is used for all the amplitudes: it is indexed (besides the partition numbers) by IN,IB,IA & KN (see glossary), and stores a real number A.

The table is filled cumulatively, starting perhaps with &overlap namelists, so amplitudes need only be entered after the namelist for the first KIND of coupling in which they appear. (So if all the amplitudes are already entered for a certain KIND of coupling, then the following namelist will be blank, to indicate no more &cfp namelists are to be read).

For KIND = 1:

General Spin Transfer (with local or non-local external form factors on FILE `INFILE' [default 4]) See section 8 for more details.

IP1
    = 0 : local form factor
1 : non-local (two-dimensional) form factor

IP2
    = 0 : read in real values (only if IP3 $\geq$ 0)
1 : read in imaginary values (only if IP3 $\geq$ 0)
2 : read in complex values (only if IP3 $\geq$ 0)

IP3
    = 3 : read data from JLM folding program jlmP, for projectile couplings only
2 : read data from JLM folding program jlmP, for target couplings only
1 : read data from charge exchange program CHEX2, with appropriate scaling.
0 : no jlmP or CHEX2 scaling factors, only P1, P2 and FSCALE
–1 : write out typical non-local grid $(R,R')$ coordinates
–2 : calculate non-local grid $(R,R')$ coordinates, and call subroutine FFNL to calculate form factor.
–3 : calculate non-local grid $(R,R')$ coordinates, call subroutine FNLSET to calculate an initial form factor, and the call FNLCC for each pair of coupled partial waves, for L-dependent factors.
–4 : call subroutine FNLREAD to read in non-local form factor, and multiplying it by the Racah-algebra factor in section 8 (except for the $1/\sqrt{4\pi}$ factor) for given IB,IA final and initial excited states. The order of form factors in the file must agree with the order called by a double loop of channels, with the `to' channel number varying more rapidly.
–5 : call subroutine FNLREAD to read in non-local form factor for given IB,IA final and initial excited states. The order of form factors in the file must agree with the order called by a double loop of channels, with the `to' channel number varying more rapidly.

P1,P2 : scaling for the real and imaginary parts (respectively).

If IP3 $\geq$ 0, read FROM FILE `INFILE' the following lines (until a blank line):

     Format 16.2: I4, 3F8.4,          I4,  2F4.0,   2I4,   A35
                NP ,HNP,RFS,FSCALE, LTR, PTR,TTR, IB,IA, COMMENT
            for NP = number of radial points
                HNP = step size
                RFS = radius of first point
                FSCALE = scaling factor to be applied
                LTR = L-transfer
                PTR = projectile spin transfer
                TTR = target spin transfer
                IB  = excited-state pair fed by coupling
                IA  = excited-state pair feeding the coupling
                COMMENT = comment for display in printout.

       then free format, repeatedly until sufficient data is read.

If IP1 = 0, read local form factor from i=1 to N
1, read successively for j=1,NLO the non-local form factors FNL(i,j), i=1 to NP [NLO = RNL / max(HNL,HCM)]

When IP3=1 for CHEX2 input, the RFS and its F8.4 is omitted from Card 16.2, with default value RFS=HNP.

For KIND = 2:

Electromagnetic one-photon couplings (for $E\lambda$ and $M\lambda$ processes).

ICTO is the gamma partition and ICFROM the particle partition. The photon must be on the `projectile' side, and the bound state between target states.

IP1 = $\lambda$ : The multipolarity of the radiation. If $\lambda >$ 0, include all multipoles 1,...,$\lambda$ permitted by parity, whereas if IP1 $<$ 0, include only the multipole $\lambda$ = abs(IP1).

IP2
   = 0,4 : Calculates both electric and magnetic couplings (reads $g$-factors from P1&P2)
1,5 : for electric only
2 : for magnetic only (reads $g$-factors from P1&P2)
4,5 : include also Siegert remnant for electric transitions

IP3: not implemented yet

P1 = projectile $g$-factor
P2 = target $g$-factor

IP4
    = 0 : direct capture only
1 : semi-direct capture only
2 : direct + semi-direct capture mechanisms.

For KIND = 3 or 4:

Single-particle excitations of the projectile (3) or target (4)

For these KINDs, ICTO is the partition of the nuclei being excited, and ICFROM is used to indicate the core partition if the single particle were removed. No couplings are generated to or from the ICFROM partition, only within ICTO partition.

IP1 = Q : The multipole order of the deforming potential due to the colliding nucleus. If Q $>$ 0, include all multipoles 0,1,...,Q permitted by parity, whereas if IP1 $<$ 0, include only the multipole Q = abs(IP1).

IP2
= 0 : Coulomb & nuclear (complex)
= 1 : nuclear (complex) only
= 2 : Coulomb only

IP3
= 0 or 10 : include all re-orientation terms
= 1 or 11 : no re-orientation terms for $Q > 0$
= 2 or 12 : ONLY re-orientation terms
= 3 or 13 : include only couplings to and from the ground state, but NOT gs reorientation,
= 4 or 14 : include diagonal couplings, and couplings to and from the ground state
= 5 or 15 : include diagonal couplings, and couplings to and from any bound state
$\geq$ 10 : read namelist &scale for complex factors [QSCALE(Q), Q=max(0,-IP1):abs(IP1)] to scale the folded form factors for multipoles Q.

P1 = FLOAT( potential KP index for fragment - target interaction)
P2 = FLOAT( potential KP index for core - target interaction)
(only SCALAR parts of the potentials P1 and P2 are used).

For KIND = 5 or 6:

Zero-range & LEA transfers

IP1 and IP2 not used.

For KIND=5,
P1 = $D_0$ - ZR coupling constant
P2 = FNRNG - Effective finite-range parameter for use in LEA (in units of fm.)

For KIND=6, use $D_0$ and FNRNG = $\sqrt{(D/D_0 - 1)/k^2}$. from the projectile bound states. With unbound states, or if IP3 = 1, use $D_0$ from state, but FNRNG = P2 from this namelist.

In both KINDs, read in &cfp namelists, noting that for KIND = 5 spectroscopic factors for the projectile are not needed, and are ignored.

Users of these interactions kinds should also pay attention to the the parameter INH in the &Fresco namelist.

For KIND = 7:

Finite-range transfers.

IP1 =
    0,-2 : POST interaction
1,-1 : PRIOR interaction (N.B. meaning of IP1 thus depends on ICTO & ICFROM!!!)
$\le$ -1 : Use $\theta$ quadrature from $\theta = \pi$ down to $\theta = 0$. (Useful for finite-range knock-on with light projectiles)
$\le$ -3 : `VCORE' interaction: Use ONLY the core-core interaction potential (Useful for finite-range knock-on with light projectiles)
2 : Surface transfer operator, on surface if final bound state $r' =$ P1. IP2 and IP3 ignored.
3 : Surface transfer operator, on surface if initial bound state $r =$ P1. (Not yet implemented)
4 : Surface transfer operator calculated as PRIOR–POST. Need also to set RSMAX for final bound state to the desired surface radius. (Implemented, but not yet correctly).
5 : Surface transfer operator calculated as POST–PRIOR. Need also to set RSMAX for initial bound state to the desired surface radius. (Not yet implemented).

IP2 =
    0 : no remnant
1 : full real remnant
-1 : full complex remnant
2 : “non-orthogonality remnant" - this works by inserting a KIND = 8 coupling namelist after this coupling, before any subsequent couplings. This is does not affect the one-step amplitudes, and is only useful if another transfer step follows this coupling.

IP3 = KPCORE : the number KP of the potential to use between the two cores, in the remnant part of the interaction potential.

If IP3=0, use as KPCORE the optical potential given for the first pair of excited states in the partition of projectile core. (this uses the observation that optical potentials tend to depend more on the projectile than the target, and must clearly be re-examined if the projectile is heavier than the target.)

P1,P2 : not used.

For KIND = 8:

Non-orthogonality supplement appropriate to a previous KIND 5,6 or 7 interaction.

IP1 =
    0 : post
1 : prior (N.B. IP1 should be the same as the previous interaction!)

IP2
$>$ 0 : read in spectroscopic factors as &cfp namelists (Only useful if you did NOT have a previous KIND 5, 6 or s7 interaction, which would have needed the amplitudes then.)
= 0 : no &cfp namelists to read.

Note that you should either use KIND=7, $\vert$IP2$\vert$=2, or use KIND=7, $\vert$IP2$\vert$=1 and a KIND=8. If you have KIND=7, $\vert$IP2$\vert$=2 and a KIND=8 namelist, then this is double counting.

&CFP namelists

Spectroscopic amplitudes for the overlaps between partitions ICTO & ICFROM already defined by a &coupling namelist:

IN, IB, IA, KN, A

 
meaning that the overlap of the composite nucleus in excitation state IB with the core nucleus in excitation state IA is the bound-state form factor KN with amplitude A. The IN=1 specifies projectile overlap, and IN=2 target overlap.

If the form factor KN mixes different IA levels, then the spectroscopic amplitudes should rather be specified in an &overlap namelist.

N.B. The amplitudes A are signed, and are NOT the spectroscopic factors, but will typically be the square roots of these factors. For transfers out of or into closed shells of N antisymmetrised nucleons, the spectroscopic factors will usually contain factors of N, so the spectroscopic amplitudes needed by FRESCO will typically need to already contain factors of $\sqrt{N}$.
The sign of A should be consistent with the spin coupling order used in the program, which is

$$(\ell,s)j, J_{core}; J_{com}$$ (12)

for binding a $\ell sj$ nucleon onto a core of spin $J_{core}$ to form $J_{com}$.
If IN$<$0, use abs(IN) in this the last &cfp namelist
If IN=0, no more &cfp namelists to be read.