Evaluation of Nuclear Matrix Elements Involving Harmonic Oscillator Wave Functions

1974 ◽  
Vol 52 (4) ◽  
pp. 324-329
Author(s):  
C. K. Scott ◽  
R. N. Singh
Keyword(s):  
Harmonic Oscillator ◽  
Nuclear Matrix ◽  
Wave Functions ◽  
Matrix Elements ◽  
Simplified Form

A simplified form of the integral of products of harmonic oscillator wave functions is presented, with application to the evaluation of common nuclear matrix elements.

scholarly journals Magnetic HexadecapoleγTransitions and Neutrino-Nuclear Responses in Medium-Heavy Nuclei

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Lotta Jokiniemi ◽  
Jouni Suhonen ◽  
Hiroyasu Ejiri
Keyword(s):  
Nuclear Matrix ◽  
Wave Functions ◽  
Matrix Elements ◽  
Heavy Nuclei ◽  
Magnetic Quadrupole ◽  
Order Of Magnitude ◽  
Nuclear Responses ◽  
Beta Decays ◽  
Gamow Teller ◽  
Phonon Model

Neutrino-nuclear responses in the form of squares of nuclear matrix elements, NMEs, are crucial for studies of neutrino-induced processes in nuclei. In this work we investigate magnetic hexadecapole (M4) NMEs in medium-heavy nuclei. The experimentally derived NMEs,MEXP(M4), deduced from observed M4γtransition half-lives are compared with the single-quasiparticle (QP) NMEs,MQP(M4), and the microscopic quasiparticle-phonon model (MQPM) NMEsMMQPM(M4). The experimentally derived M4 NMEs are found to be reduced by a coefficientk≈0.29with respect toMQP(M4) and byk≈0.33with respect toMMQPM(M4). The M4 NMEs are reduced a little by the quasiparticle-phonon correlations of the MQPM wave functions but mainly by other nucleonic and nonnucleonic correlations which are not explicitly included in the MQPM. The found reduction rates are of the same order of magnitude as those for magnetic quadrupoleγtransitions and Gamow-Teller (GT) and spin-dipole (SD)βtransitions. The impacts of the found reduction coefficients on the magnitudes of the NMEs involved in astroneutrino interactions and neutrinoless double beta decays are discussed.

The β+ Decay of 234Np and Other Isospin-Forbidden 0+→ 0+ Fermi Transitions

1984 ◽  
Vol 39 (12) ◽  
pp. 1168-1171
Author(s):  
C. T. Yap ◽  
E. L. Saw
Keyword(s):  
Nuclear Matrix ◽  
Coulomb Potential ◽  
Deformation Parameter ◽  
Theoretical Calculations ◽  
Wave Functions ◽  
Matrix Elements ◽  
Β Decay ◽  
A Value ◽  
Experimental Values ◽  
Good Agreement

Although experimental values of the Fermi nuclear matrix elements vary widely from about 1 × 10-3 to 40 × 10-3 for isospin-forbidden 0+→0+ β transitions, theoretical calculations using the Coulomb potential and Nilsson wave functions yielded values of MF in reasonably good agreement, except that of 234Np. However, our calculation of MF for this decay as a function of the deformation parameter β yielded a value of MF in good agreement with experiment for values of β between 0.1 and 0.2.

AN ALGEBRAIC APPROACH TO A HARMONIC OSCILLATOR PLUS AN INVERSE SQUARE POTENTIAL IN TWO DIMENSIONS

2005 ◽  
Vol 20 (24) ◽  
pp. 5663-5670 ◽  
Author(s):  
SHI-HAI DONG ◽  
GUO-HUA SUN ◽  
M. LOZADA-CASSOU
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Algebraic Approach ◽  
Two Dimensions ◽  
Wave Functions ◽  
Matrix Elements ◽  
Ladder Operators ◽  
Radial Wave ◽  
Commutation Relations ◽  
The Matrix

The exact solutions of the Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained in two dimensions. We construct the ladder operators directly from the radial wave functions and find that these operators satisfy the commutation relations of an SU (1, 1) group. We obtain the explicit expressions of the matrix elements for some related functions ρ and [Formula: see text] with ρ = r2. We also explore another symmetry between the eigenvalues E(r) and E(ir) by substituting r→ir.

GT strengths studied by (3He, t) reactions and nuclear matrix elements for double beta decays

1997 ◽  
Vol 394 (1-2) ◽  
pp. 23-28 ◽  
Author(s):  
Hidetoshi Akimune ◽  
Hiroyasu Ejiri ◽  
Mamoru Fujiwara ◽  
Izuru Daito ◽  
Toru Inomata ◽  
...  
Keyword(s):  
Nuclear Matrix ◽  
Matrix Elements ◽  
Beta Decays
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