# Pair correlation in deformed neutron-drip-line nuclei: The eigenphase formalism and asymptotic behavior

## Abstract

The Hartree-Fock-Bogoliubov (HFB) equation for deformed nuclei in a simplified model is solved in coordinate space with correct asymptotic boundary conditions, in order to study the pair correlation in nuclei close to the neutron drip line. The eigenphase formalism is applied, when the upper components of HFB radial wave functions are continuum wave functions. Calculated occupation probabilities of various Nilsson orbits in the HFB ground state vary smoothly from the region of the upper components being bound wave functions to that of those being continuum wave functions. It is shown that weakly-bound or resonance-like {omega}{sup {pi}}=1/2{sup +} Nilsson orbits contribute little to the occupation probability of the HFB ground state, while the contribution by the orbits with a large value of {omega}, of which the smallest possible orbital-angular-momentum is neither 0 nor 1, may be approximately estimated using the BCS formula.

- Authors:

- Division of Mathematical Physics, Lund Institute of Technology at the University of Lund, Lund (Sweden)
- (Denmark)

- Publication Date:

- OSTI Identifier:
- 20771443

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevC.73.044317; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BCS THEORY; BOUNDARY CONDITIONS; CORRELATIONS; DEFORMED NUCLEI; EIGENFUNCTIONS; EIGENVALUES; GROUND STATES; HARTREE-FOCK METHOD; HARTREE-FOCK-BOGOLYUBOV THEORY; NEUTRONS; ORBITAL ANGULAR MOMENTUM; PROBABILITY; RESONANCE; SHELL MODELS; WAVE FUNCTIONS

### Citation Formats

```
Hamamoto, Ikuko, and Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100.
```*Pair correlation in deformed neutron-drip-line nuclei: The eigenphase formalism and asymptotic behavior*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevC.73.044317.

```
Hamamoto, Ikuko, & Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100.
```*Pair correlation in deformed neutron-drip-line nuclei: The eigenphase formalism and asymptotic behavior*. United States. doi:10.1103/PhysRevC.73.044317.

```
Hamamoto, Ikuko, and Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100. Sat .
"Pair correlation in deformed neutron-drip-line nuclei: The eigenphase formalism and asymptotic behavior". United States.
doi:10.1103/PhysRevC.73.044317.
```

```
@article{osti_20771443,
```

title = {Pair correlation in deformed neutron-drip-line nuclei: The eigenphase formalism and asymptotic behavior},

author = {Hamamoto, Ikuko and Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100},

abstractNote = {The Hartree-Fock-Bogoliubov (HFB) equation for deformed nuclei in a simplified model is solved in coordinate space with correct asymptotic boundary conditions, in order to study the pair correlation in nuclei close to the neutron drip line. The eigenphase formalism is applied, when the upper components of HFB radial wave functions are continuum wave functions. Calculated occupation probabilities of various Nilsson orbits in the HFB ground state vary smoothly from the region of the upper components being bound wave functions to that of those being continuum wave functions. It is shown that weakly-bound or resonance-like {omega}{sup {pi}}=1/2{sup +} Nilsson orbits contribute little to the occupation probability of the HFB ground state, while the contribution by the orbits with a large value of {omega}, of which the smallest possible orbital-angular-momentum is neither 0 nor 1, may be approximately estimated using the BCS formula.},

doi = {10.1103/PhysRevC.73.044317},

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

number = 4,

volume = 73,

place = {United States},

year = {Sat Apr 15 00:00:00 EDT 2006},

month = {Sat Apr 15 00:00:00 EDT 2006}

}