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Manuscript Title: Model space dimensionalities for multiparticle fermion systems.
Authors: J.P. Draayer, H.T. Valdes
Program title: SU2DIMPH
Catalogue identifier: AABN_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 36(1985)313
Programming language: Fortran.
Computer: IBM 3081-D24.
Operating system: MVS/SP 1.3.3, AOS/VS, DOS 2.0.
RAM: 116K words
Peripherals: disc.
Keywords: Atomic physics, Nuclear physics, Statistical spectroscopy, Distributions spectral, Level density, Configuration Partitioning, Configuration averages, Fixed-j, Fixed-jt, R3 multiplicity, Su2 multiplicity, Jj-coupling, Ls-coupling, M-distributions, J-distributions, M-scheme, Theoretical methods.
Classification: 2.9, 17.16.

Nature of problem:
A menu driven program for determining the dimensionalities of fixed-(J) (or (J,T)) model spaces built by distributing identical fermions (electrons, neutrons, protons) or two distinguishable fermion types (neutron-proton, isospin formalisms) among any mixture of positive and negative parity spherical orbitals is presented. The algorithm, built around the elementary difference formula d (J) = d(M=J) - d(M=J+1), takes full advantage of M -M and particle-hole symmetries. A 96K version of the program suffices for as complicated a case as d((+1/2,+3/2,+5/2,+7/2,-11/2)n=26J =2+,T=7) = 210,442,716,722 found in the oh valence space of 126 56Ba70. The program calculates the total fixed-(Jphi) or fixed-(Jphi,T) dimenionality of a model space generated by distributing a specified number of fermions among a set of input positive and negative parity (phi) spherical (j) orbitals. The user is queried at each step to select among various options: 1. Formalism - Identical particle, neutron-proton, isospin. 2. Orbits - Number, +/- 2*J of all orbits. 3. Limits - Minimum/maximum number of particles of each parity. 4. Specifics - Number of particles, +/-2*J (total), 2*T. 5. Continue - Same orbit structure, new case, quit. Though designed for nuclear applications (jj-coupling), the program can be used in the atomic case (LS-coupling) so long as half integer spin values (j = l+- 1/2) are input for the valence orbitals. Multiple occurrences of a given j value are properly taken into account. A minor extension provides labelling information for a generalized seniority classification scheme. The program logic is an adaptation of methods used in statistical spectroscopy to evaluate configuration averages. Indeed, the need for fixed symmetry level densities in distribution spectral theory motivated this work. The methods extend to other group structures where there are M-like additive quantum labels.

Solution method:
The algorithm is based on the elementary difference formula, dl(J)= d(M=J) - d(M=J+1), where d(M) is the number of ways in which a state with total angular momentum projection M can occur. The d(M) are determined using m-scheme configuration results. Specifically, if n- = (n1,n2,...,nk) specifies a particular distribution of the n=Sigma alpha n alpha particles among the m levels (alpha=2m, k=2mmax= 2jmax) and d(n-,M)=Phi alpha (N alpha n alpha) where N alpha is the maximum occupancy of the m-th level, then d(M)=d(n,M)=Sigma' n- d(n-,M) where the prime on the summation denotes a restriction to those n- for which Sigma alpha mn alpha=M. Actually, to save storage and enhance the speed of the program, configuration dimensionalities are generated for m>0 levels only. A slight extension of the above then yields d(M)= Sigma n',m' d(n',M') * d(n-n',M-M'). In addition, the particle-hole symmetry d(n~,M~) = d(n,m) where n~=nmax-n and M~=Mmax-M is used to reduce to a minimum the required number of d(n,M) values.

Restrictions:
The single precision version (32-bit word length) of the program yields correct results for d<~10**6. Introducing double precision increases this to d<~10**14. The program size is fixed by seven constants, the number of j-orbits (<=32), the number of m-levels (<=128), the number of distinct (n,M) combinations (<=256), etc. Internal checks are used to alert the user to dimension overflow conditions. Program statistics on these parameters (limit/usage) are output for each case executed. The limits can be easily adjusted either upward or downward.

Running time:
Run times scale roughly with the total dimensionality, ranging from just a few seconds for d~10**2 to several minutes for d~10**6 on the IBM PC/ XT. The test run executes in 7.2 s on the IBM 3081 mainframe, 20.3 s on the DG MV/10000, and takes 38 m on the IBM PC/XT (no floating point enhancements).