Large Scale Shell Model Calculations
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The purpose of computational physics is not to crunch numbers but to gain insight. Exponential growth in computing power. We have redefined the class of problems that we can solve. Supercomputers ---- Parallel machines. New algorithms and existing codes need modifications.
Many body problem. I.
Interaction
II. Model Space III. Method
Two approaches Mean Field. II. Shell Model I.
H|ψ>=E |ψ>
The nuclear Shell-Model is the most general microscopic nuclear model and is in principle able to describe all properties of nuclei.
Nuclear Shell-Model calculations in large and realistic single-particle (s.p.) model spaces are, however, very difficult to make due to the extremely large Hilbert space dimensions involved.
The continuous increase in computing power has made it possible to make progressively larger nuclear calculations in restricted model spaces. Currently existing nuclear SMC methods/programs make it possible to calculate nuclear wave functions exactly in the model spaces sd and pf and in pf5/2g9/2 model space with some what truncated calculations.
Nucleons in a mean potential interacting through residual interactions Single particle energy （ SPE) Two-body interaction （ TBME)
H = ∑ ε a na + a
∑
a ≤ b , c ≤ d , JT
+ V (abcd ; JT )AJT ( ab) AJT (cd )
na … number operators of orbit a † AabJT = (1 + δ ab ) −1/ 2 ca† cb†
JT
Closed core + valence shell 0ħω space p-shell
4
He
+
0p3/2, 0p1/2
sd-shell
16
O
+
0d5/2, 1s1/2, 0d3/2
pf-shell
40
Ca
+
0f7/2, 1p3/2, 1p1/2, 0f5/2
…
nħω space p-sd, sd-pf, … For unstable nuclei, large deformation, …
Shell Model
9. OUR CODE (IUAC-KU) : J- scheme [2005-2006]
The most basic SMC method is the m-scheme method that uses bare Slater determinants of spherically symmetric s.p. orbit configurations as its many-body basis states. The basic problem with the m-scheme SMC is that the Slater determinant basis dimension is maximal and therefore a lot of storage (from gigabytes to tens of gigabytes) is needed for each calculated Lanczos basis vector in large-scale calculations. A common method to reduce the large matrix dimensions of the m-scheme SMC is to use the existing symmetries of the nuclear Hamiltonian. The j-scheme SMC method uses angular momentum projected many-body basis states, but does not have good isospin, and is used in our code (To be published). Compared to the m-scheme the j-scheme typically reduces the SMC dimensions by two orders of magnitude for low-spin states and less for high-spin states. This property makes it most suitable for low-spin states, such as the ground states of double-even nuclei..
ADAPTATION OF ALGORITHMS TO PARALLEL PLATFORM
The computer code is written in Fortran Language. Compilation and execution requires a Fortran 77 compiler (in build under lynx environment) and at least 3GB of RAM for sd-shell of system hardware.
Program
Structure
Input data files. ( dimen.shell,sjsme.inp,hamilt.inp) Program files.(basis.f, multibase.f , cfp.f etc) Out-put files. ( *.out)
Due to moderate Computational facility , we addressed some problems in sd-shell.
We were trying to address the structure of S33(16,17),Cl36(17,19) and P31(15,16) with Si28(14,14) core. The neutron rich nuclei in the fp shell region are at the focus of attention of the nuclear physics community at present. Unstable nuclei in this region exhibit many new phenomenon such as appearance of new magic numbers and disappearance of well established ones, softening of core at N=28, interplay of collective and single particle properties etc. Neutron rich fp shell nuclei are also of special interest in astrophysics such as the electron capture rate in supernovae explosion. A large number of neutron rich nuclei can be populated by means of binary reactions such as multi-nucleon transfer and deep inelastic collisions with stable beam. Such reactions combined with modern detector arrays have increased substantially the available data on nuclei far from stability Experimental data on the excited states of neutron rich unstable isotopes of Ca, Ti and Cr has been made available in recent past (NNDC World Wide Web)
For SMC – Shared system would be ideal choice( many cores and a huge memory). We shall be also using HFODD, which solves HFB equations in three dimensions with Skyrme Density Functional. The code is parallel and I am running it on two core machine (laptop).
Leonardo da vinci
The purpose of computational physics is not to crunch numbers but to gain insight. Exponential growth in computing power. We have redefined the class of problems that we can solve. Supercomputers ---- Parallel machines. New algorithms and existing codes need modifications.
Many body problem. I.
Interaction
II. Model Space III. Method
Two approaches Mean Field. II. Shell Model I.
H|ψ>=E |ψ>
The nuclear Shell-Model is the most general microscopic nuclear model and is in principle able to describe all properties of nuclei.
Nuclear Shell-Model calculations in large and realistic single-particle (s.p.) model spaces are, however, very difficult to make due to the extremely large Hilbert space dimensions involved.
The continuous increase in computing power has made it possible to make progressively larger nuclear calculations in restricted model spaces. Currently existing nuclear SMC methods/programs make it possible to calculate nuclear wave functions exactly in the model spaces sd and pf and in pf5/2g9/2 model space with some what truncated calculations.
Nucleons in a mean potential interacting through residual interactions Single particle energy （ SPE) Two-body interaction （ TBME)
H = ∑ ε a na + a
∑
a ≤ b , c ≤ d , JT
+ V (abcd ; JT )AJT ( ab) AJT (cd )
na … number operators of orbit a † AabJT = (1 + δ ab ) −1/ 2 ca† cb†
JT
Closed core + valence shell 0ħω space p-shell
4
He
+
0p3/2, 0p1/2
sd-shell
16
O
+
0d5/2, 1s1/2, 0d3/2
pf-shell
40
Ca
+
0f7/2, 1p3/2, 1p1/2, 0f5/2
…
nħω space p-sd, sd-pf, … For unstable nuclei, large deformation, …
Shell Model
9. OUR CODE (IUAC-KU) : J- scheme [2005-2006]
The most basic SMC method is the m-scheme method that uses bare Slater determinants of spherically symmetric s.p. orbit configurations as its many-body basis states. The basic problem with the m-scheme SMC is that the Slater determinant basis dimension is maximal and therefore a lot of storage (from gigabytes to tens of gigabytes) is needed for each calculated Lanczos basis vector in large-scale calculations. A common method to reduce the large matrix dimensions of the m-scheme SMC is to use the existing symmetries of the nuclear Hamiltonian. The j-scheme SMC method uses angular momentum projected many-body basis states, but does not have good isospin, and is used in our code (To be published). Compared to the m-scheme the j-scheme typically reduces the SMC dimensions by two orders of magnitude for low-spin states and less for high-spin states. This property makes it most suitable for low-spin states, such as the ground states of double-even nuclei..
ADAPTATION OF ALGORITHMS TO PARALLEL PLATFORM
The computer code is written in Fortran Language. Compilation and execution requires a Fortran 77 compiler (in build under lynx environment) and at least 3GB of RAM for sd-shell of system hardware.
Program
Structure
Input data files. ( dimen.shell,sjsme.inp,hamilt.inp) Program files.(basis.f, multibase.f , cfp.f etc) Out-put files. ( *.out)
Due to moderate Computational facility , we addressed some problems in sd-shell.
We were trying to address the structure of S33(16,17),Cl36(17,19) and P31(15,16) with Si28(14,14) core. The neutron rich nuclei in the fp shell region are at the focus of attention of the nuclear physics community at present. Unstable nuclei in this region exhibit many new phenomenon such as appearance of new magic numbers and disappearance of well established ones, softening of core at N=28, interplay of collective and single particle properties etc. Neutron rich fp shell nuclei are also of special interest in astrophysics such as the electron capture rate in supernovae explosion. A large number of neutron rich nuclei can be populated by means of binary reactions such as multi-nucleon transfer and deep inelastic collisions with stable beam. Such reactions combined with modern detector arrays have increased substantially the available data on nuclei far from stability Experimental data on the excited states of neutron rich unstable isotopes of Ca, Ti and Cr has been made available in recent past (NNDC World Wide Web)
For SMC – Shared system would be ideal choice( many cores and a huge memory). We shall be also using HFODD, which solves HFB equations in three dimensions with Skyrme Density Functional. The code is parallel and I am running it on two core machine (laptop).
Leonardo da vinci
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