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SUMMARY:POSSIBILITIES TO IMPROVE VARIATIONAL  CALCULATIONS USING OSCILLATO
 R BASIS
DTSTART;VALUE=DATE-TIME:20220715T070000Z
DTEND;VALUE=DATE-TIME:20220715T072000Z
DTSTAMP;VALUE=DATE-TIME:20260519T130623Z
UID:indico-contribution-241@events.sinp.msu.ru
DESCRIPTION:Speakers: Vasily Kulikov (Skobeltsyn Institute of Nuclear Phys
 ics\, Lomonosov Moscow State University)\nOscillator basis is widely used 
 in nuclear structure studies\, e. g.\, within *ab initio* No-Core Shell Mo
 del (NCSM) [1]. A problem faced by the NCSM calculations is an exponential
  grows of the many-body basis dimension and of the number of non-zero Hami
 ltonian matrix elements which restricts the accuracy of the results and th
 e NCSM applicability to heavier nuclei. This difficulty can be overcome by
  using the complete Hamiltonian matrix up to some excitation quanta *N*_{m
 ax} and extending it to a larger excitation quanta *N'*_{max} by kinetic e
 nergy *T* matrix elements only (*T* extension). The *T* extension can be c
 onsidered as a simplified version of the Symmetry-Adapted NCSM (SA-NCSM) [
 2] which utilizes the Sp(3\,R) symmetry to extend the Hamiltonian matrix s
 ince T is one of the Sp(3\,R) generator. The *T*-extended Hamiltonian matr
 ix has an essentially smaller number of non-zero matrix elements and impro
 ves predictions for binding energies. The Hamiltonian matrix extended up t
 o infinite *N'*_{max} in a channel that is supposed to dominate in the asy
 mptotics of the wave function of bound state of interest\, can be used to 
 calculate the S matrix by means of the HORSE formalism [3] and to locate n
 umerically its pole associated with the bound state that makes it possible
  to obtain a very accurate prediction for the binding energy and asymptoti
 c normalization coefficient (ANC). The utilization of the complete HORSE f
 ormalism within the NCSM is impractical because it requires calculation of
  extremely large number of the NCSM eigenstates\; however\, one can use it
 s simplified version SS-HORSE [4] to design an extrapolation technique for
  binding energies and ANC. An interesting and important convergence accele
 ration of the above approaches is the smoothing of potential energy matrix
  elements suggested in Ref. [5]. We illustrate the above possibilities usi
 ng a model problem.\n\n 1. B. R. Barrett\, P. Navrátil\, and J. P. Vary\,
  Prog. Part. Nucl. Phys. **69**\, 131 (2013).\n 2. K. D. Launey\, T. Dytry
 ch\, and J. P. Draayer\, Prog. Part. Nucl. Phys. **89**\, 101 (2016).\n 3.
  J. M. Bang\, A. I. Mazur\, A. M. Shirokov\, Yu. F. Smirnov\, and S. A. Za
 ytsev\, Ann. Phys. (N.Y.) **280**\, 299 (2000). \n 4. A. M. Shirokov\, A. 
 I. Mazur\, I. A. Mazur and J. P. Vary\, Phys. Rev. C **94**\, 064320 (2016
 ).\n 5. B. Gyarmati\, A. T. Kruppa\, and J. Révai\,  Nucl. Phis A **326**
 \, 119 (1979).\n\nhttps://events.sinp.msu.ru/event/8/contributions/241/
LOCATION: Физический ф-т\, 5-19
URL:https://events.sinp.msu.ru/event/8/contributions/241/
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