Wave function of $^9$Be in the three-body (alpha-alpha-n)-model
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914899057180672 |
|---|---|
| author | Rakityansky, S. A. |
| author_facet | Rakityansky, S. A. |
| contents | A simple analytic expression of the three-body wave function describing the system $(ααn)$ in the ground state $\frac{3}{2}^-$ of ${}^9\mathrm{Be}$ is obtained. In doing this, it is assumed that the $α$ particles interact with each other via the $S$-wave Ali-Bodmer potential including the Coulomb term, and the neutron-$α$ forces act only in the $P$-wave state. This wave function is constructed by trial and error method via solving in this way a kind of inverse problem when the two-body $αα$ potential is recovered from a postulated three-body wave function. As a result, the wave function is an exact solution of the corresponding three-body Schrödinger equation for experimentally known binding energy and for the $αα$ potential whose difference from the Ali-Bodmer one is minimized by varying the adjustable parameters which the postulated wave function depends on. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17371 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wave function of $^9$Be in the three-body (alpha-alpha-n)-model Rakityansky, S. A. Nuclear Theory A simple analytic expression of the three-body wave function describing the system $(ααn)$ in the ground state $\frac{3}{2}^-$ of ${}^9\mathrm{Be}$ is obtained. In doing this, it is assumed that the $α$ particles interact with each other via the $S$-wave Ali-Bodmer potential including the Coulomb term, and the neutron-$α$ forces act only in the $P$-wave state. This wave function is constructed by trial and error method via solving in this way a kind of inverse problem when the two-body $αα$ potential is recovered from a postulated three-body wave function. As a result, the wave function is an exact solution of the corresponding three-body Schrödinger equation for experimentally known binding energy and for the $αα$ potential whose difference from the Ali-Bodmer one is minimized by varying the adjustable parameters which the postulated wave function depends on. |
| title | Wave function of $^9$Be in the three-body (alpha-alpha-n)-model |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2407.17371 |