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A differential equation for the transition probability B(E2)↑ and the resulting recursion relations connecting even–even nuclei

Abstract

We obtain here a new relation for the reduced electric quadrupole transition probability B(E2)↑ of a given nucleus in terms of its derivatives with respect to neutron and proton numbers based on a similar local energy relation in the Infinite Nuclear Matter (INM) model of atomic nuclei, which is essentially built on the foundation of the Hugenholtz–Van Hove (HVH) theorem of many-body theory. Obviously, such a relation in the form of a differential equation is expected to be more powerful than the usual algebraic difference equations. Although the relation for B(E2)↑ has been perceived simply on the basis of a corresponding differential equation for the local energy in the INM model, its theoretical foundation otherwise has been clearly demonstrated. We further exploit the differential equation in using the very definitions of the derivatives to obtain two different recursion relations for B(E2)↑, connecting in each case three neighboring even–even nuclei from lower to higher mass numbers and vice versa. We demonstrate their numerical validity using available data throughout the nuclear chart and also explore their possible utility in predicting B(E2)↑ values. (author)
Authors:
Pattnaik, S.; [1]  Nayak, R. C. [2] 
  1. Taratarini College, Purusottampur, Ganjam, Odisha (India)
  2. Department of Physics, Berhampur University, Brahmapur-760007 (India)
Publication Date:
Apr 15, 2014
Product Type:
Journal Article
Resource Relation:
Journal Name: International Journal of Modern Physics E; Journal Volume: 23; Journal Issue: 4
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; DIFFERENTIAL EQUATIONS; EVEN-EVEN NUCLEI; MASS NUMBER; NUCLEAR MATTER; QUADRUPOLES; VAN HOVE-HUGENHOLTZ THEORY
OSTI ID:
22288504
Country of Origin:
Singapore
Language:
English
Other Identifying Numbers:
Journal ID: ISSN 0218-3013; TRN: SG1400491109938
Availability:
Available from DOI: http://dx.doi.org/10.1142/S0218301314500220
Submitting Site:
INIS
Size:
[14 page(s)]
Announcement Date:
Dec 19, 2014

Citation Formats

Pattnaik, S., and Nayak, R. C. A differential equation for the transition probability B(E2)↑ and the resulting recursion relations connecting even–even nuclei. Singapore: N. p., 2014. Web. doi:10.1142/S0218301314500220.
Pattnaik, S., & Nayak, R. C. A differential equation for the transition probability B(E2)↑ and the resulting recursion relations connecting even–even nuclei. Singapore. doi:10.1142/S0218301314500220.
Pattnaik, S., and Nayak, R. C. 2014. "A differential equation for the transition probability B(E2)↑ and the resulting recursion relations connecting even–even nuclei." Singapore. doi:10.1142/S0218301314500220. https://www.osti.gov/servlets/purl/10.1142/S0218301314500220.
@misc{etde_22288504,
title = {A differential equation for the transition probability B(E2)↑ and the resulting recursion relations connecting even–even nuclei}
author = {Pattnaik, S., and Nayak, R. C.}
abstractNote = {We obtain here a new relation for the reduced electric quadrupole transition probability B(E2)↑ of a given nucleus in terms of its derivatives with respect to neutron and proton numbers based on a similar local energy relation in the Infinite Nuclear Matter (INM) model of atomic nuclei, which is essentially built on the foundation of the Hugenholtz–Van Hove (HVH) theorem of many-body theory. Obviously, such a relation in the form of a differential equation is expected to be more powerful than the usual algebraic difference equations. Although the relation for B(E2)↑ has been perceived simply on the basis of a corresponding differential equation for the local energy in the INM model, its theoretical foundation otherwise has been clearly demonstrated. We further exploit the differential equation in using the very definitions of the derivatives to obtain two different recursion relations for B(E2)↑, connecting in each case three neighboring even–even nuclei from lower to higher mass numbers and vice versa. We demonstrate their numerical validity using available data throughout the nuclear chart and also explore their possible utility in predicting B(E2)↑ values. (author)}
doi = {10.1142/S0218301314500220}
journal = {International Journal of Modern Physics E}
issue = {4}
volume = {23}
journal type = {AC}
place = {Singapore}
year = {2014}
month = {Apr}
}