Numerical computation of an integral appearing in the Fröman-Fröman phase-integral formula for calculation of quantal matrix elements without the use of wave functions

1977 ◽  
Vol 24 (1) ◽  
pp. 81-95 ◽  
Author(s):  
Sven-Åke Gustafson ◽  
Staffan Lindahl
Keyword(s):  
Numerical Computation ◽  
Integral Formula ◽  
Wave Functions ◽  
Matrix Elements ◽  
Phase Integral

scholarly journals Optics of Chromites and Charge-Transfer Transitions

2008 ◽  
Vol 2008 ◽  
pp. 1-4 ◽  
Author(s):  
Andrei V. Zenkov
Keyword(s):  
Charge Transfer ◽  
Simple Structure ◽  
Electric Dipole Transition ◽  
Wave Functions ◽  
Final States ◽  
Matrix Elements ◽  
Cluster Approach ◽  
Electron Wave ◽  
Charge Transfer Transitions ◽  
Transition Modeling

Specific features of the charge-transfer (CT) states and O2p→Cr3d transitions in the octahedral (CrO6)9− complex are considered in the cluster approach. The reduced matrix elements of the electric-dipole transition operator are calculated on many-electron wave functions of the complex corresponding to the initial and final states of a CT transition. Modeling the optic spectrum of chromites has yielded a complicated CT band. The model spectrum is in satisfactory agreement with experimental data which demonstrates the limited validity of the generally accepted concept of a simple structure of CT spectra.

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.

Inelastic electric and magnetic electron scattering form factors of 24Mg nucleus: Role of g factors

2017 ◽  
Vol 26 (05) ◽  
pp. 1750032 ◽  
Author(s):  
Anwer A. Al-Sammarraie ◽  
M. L. Inche Ibrahim ◽  
Muna Ahmed Saeed ◽  
Fadhil I. Sharrad ◽  
Hasan Abu Kassim
Keyword(s):  
Experimental Data ◽  
Electron Scattering ◽  
Form Factors ◽  
Wave Functions ◽  
Matrix Elements ◽  
Model Hamiltonian ◽  
Transverse Electron ◽  
Magnetic Electron ◽  
Good Agreement

The electric and magnetic transitions in the [Formula: see text]Mg nucleus are studied based on the calculations of the longitudinal and the transverse electron scattering form factors. The universal sd-shell model Hamiltonian (USDA) is used for calculations. The wave functions of radial single-particle matrix elements are calculated using the Skyrme potential. For the longitudinal form factors, a good agreement is obtained between the calculations and the experimental data. For the transverse form factors, the effective [Formula: see text] factors are made as adjustable parameters in order to describe the experimental data.

scholarly journals Tunneling matrix elements with antiferromagnetic Gutzwiller wave functions

2011 ◽  
Vol 83 (16) ◽  
Author(s):  
Andrea Di Ciolo ◽  
Luca F. Tocchio ◽  
Claudius Gros
Keyword(s):  
Wave Functions ◽  
Matrix Elements

Collective motion in the nuclear shell model III. The calculation of spectra

1963 ◽  
Vol 272 (1351) ◽  
pp. 557-577 ◽  
Keyword(s):  
Shell Model ◽  
Collective Motion ◽  
Mass Region ◽  
Wave Functions ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
One Dimensional ◽  
The One ◽  
Nuclear Shell ◽  
Main Pattern

A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U 2- . For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to 24 Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U 3 representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 < A < 40.

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