# Exact formulation and solution of the nuclear eigenvalue problem in a microscopic multiphonon space

## Abstract

We propose a method for solving exactly the nuclear eigenvalue problem within a multiphonon space constructed out of Tamm-Dancoff phonons. The method consists in deriving, within a given n-phonon subspace, a set of equations, of simple structure for any n, which are solved iteratively, starting from the particle-hole vacuum, to yield a set of states covering a multiphonon space up to an arbitrary number of phonons. The intrinsic redundancy of the set so generated is removed completely and exactly by a simple and efficient prescription. Such a multiphonon basis reduces the Hamiltonian into diagonal blocks plus residual off-diagonal terms of simple form. Its diagonalization becomes straightforward and yields exact eigensolutions. {sup 16}O is adopted as numerical test ground.

- Authors:

- Dipartimento di Scienze Fisiche, Universita di Napoli Federico II and Istituto Nazionale di Fisica Nucleare, Monte S. Angelo, via Cintia, I-80126 Naples (Italy)
- Institute of Particle and Nuclear Physics, Charles University, V Holesovickach 2, CZ-18000 Prague 8 (Czech Republic)

- Publication Date:

- OSTI Identifier:
- 20995205

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevC.75.044312; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENVALUES; HAMILTONIANS; MATHEMATICAL SOLUTIONS; OXYGEN 16; PARTICLES; PHONONS; REDUNDANCY

### Citation Formats

```
Andreozzi, F., Iudice, N. Lo, Porrino, A., Knapp, F., and Kvasil, J.
```*Exact formulation and solution of the nuclear eigenvalue problem in a microscopic multiphonon space*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVC.75.044312.

```
Andreozzi, F., Iudice, N. Lo, Porrino, A., Knapp, F., & Kvasil, J.
```*Exact formulation and solution of the nuclear eigenvalue problem in a microscopic multiphonon space*. United States. doi:10.1103/PHYSREVC.75.044312.

```
Andreozzi, F., Iudice, N. Lo, Porrino, A., Knapp, F., and Kvasil, J. Sun .
"Exact formulation and solution of the nuclear eigenvalue problem in a microscopic multiphonon space". United States.
doi:10.1103/PHYSREVC.75.044312.
```

```
@article{osti_20995205,
```

title = {Exact formulation and solution of the nuclear eigenvalue problem in a microscopic multiphonon space},

author = {Andreozzi, F. and Iudice, N. Lo and Porrino, A. and Knapp, F. and Kvasil, J.},

abstractNote = {We propose a method for solving exactly the nuclear eigenvalue problem within a multiphonon space constructed out of Tamm-Dancoff phonons. The method consists in deriving, within a given n-phonon subspace, a set of equations, of simple structure for any n, which are solved iteratively, starting from the particle-hole vacuum, to yield a set of states covering a multiphonon space up to an arbitrary number of phonons. The intrinsic redundancy of the set so generated is removed completely and exactly by a simple and efficient prescription. Such a multiphonon basis reduces the Hamiltonian into diagonal blocks plus residual off-diagonal terms of simple form. Its diagonalization becomes straightforward and yields exact eigensolutions. {sup 16}O is adopted as numerical test ground.},

doi = {10.1103/PHYSREVC.75.044312},

journal = {Physical Review. C, Nuclear Physics},

number = 4,

volume = 75,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}