APPROXIMATE |∆I| = 1/2 RULE IN K → ππ DECAYS FROM ASYMPTOTIC QUARK-LINE DIAGRAM APPROACH

1990 ◽  
Vol 05 (29) ◽  
pp. 2423-2430 ◽  
Author(s):  
K. TERASAKI ◽  
S. ONEDA
Keyword(s):  
Selection Rule ◽  
Matrix Elements ◽  
Text Type ◽  
Line Diagram ◽  
Diagram Approach ◽  
Quark Line

Approximate |∆I| = 1/2 rule in K → ππ decays is studied from a new dynamical perspective in which quark-line diagrams should only be associated with asymptotic single-hadron matrix elements of [Formula: see text], and not with the whole amplitude. The asymptotic matrix elements of [Formula: see text] taken between ordinary [Formula: see text] mesons are found to satisfy the strict |∆I| = 1/2 rule. However, the contribution of the four-quark (QQ)[Formula: see text] type mesons leads explicitly to a small violation of the selection rule.

Analytical formulas for the Stark effect on intensity of hydrogen radiation lines

2003 ◽  
Vol 81 (5) ◽  
pp. 755-769 ◽  
Author(s):  
A A Kamenski ◽  
V D Ovsiannikov
Keyword(s):  
Perturbation Theory ◽  
Green Function ◽  
Field Strength ◽  
Stark Effect ◽  
Selection Rule ◽  
Magnetic Quantum Number ◽  
Matrix Elements ◽  
Analytical Formulas ◽  
Degenerate States ◽  
Analytical Expressions

A regular method for deriving the consecutive terms of a series in powers of field strength F for the intensities of hydrogen radiation lines is presented both analytically and numerically. Specific modification of the perturbation theory for degenerate states and the Sturm-series expansion for the completely reduced Coulomb–Green function in parabolic coordinates are used to derive simple analytical formulas for matrix elements and the intensities of the radiation transitions between circular states. Particular cases of transitions between the closest Rydberg levels are presented and discussed in detail. Analytical expressions are also derived for the quadrupole matrix elements, which may contribute to the probability of σ-transitions with the selection rule for the magnetic quantum number Δm = ±1 and determine the probability of the dipole-forbidden radiation transitions between Stark levels with Δm = ±2. PACS Nos.: 32.60.+i, 32.70.–n, 32.70.Fw

The diamagnetic effect on the intensity of helium radiation lines

2002 ◽  
Vol 80 (11) ◽  
pp. 1391-1399 ◽  
Author(s):  
V D Ovsiannikov ◽  
V V Chernushkin
Keyword(s):  
Magnetic Field ◽  
Strong Magnetic Field ◽  
Selection Rule ◽  
Matrix Elements ◽  
Line Intensities ◽  
Forbidden Transitions ◽  
Field Action ◽  
Diamagnetic Effect

The changes of the radiation matrix elements, probabilities, and line intensities in a strong magnetic field are studied for the helium lines, corresponding to transitions between Zeeman manifolds with |m| [Formula: see text] 3. The effect of a selective field action on radiation lines is discovered that may reduce and enhance corresponding matrix elements and induce the dipole-forbidden transitions with the selection rule |Δl| = 3. PACS Nos.: 32.60+i, 32.70Fw, 32.30-r

Matrix element calculation and a selection rule in the unitary group approach

1985 ◽  
Vol 63 (9) ◽  
pp. 1151-1156 ◽  
Author(s):  
A. Lev ◽  
M. Schlesinger ◽  
G. W. F. Drake ◽  
R. D. Kent
Keyword(s):  
Matrix Element ◽  
Atomic Structure ◽  
Unitary Group ◽  
Selection Rule ◽  
Closed Form Expression ◽  
Matrix Elements ◽  
Element Calculation ◽  
Form Expression ◽  
Group Approach ◽  
Unitary Group Approach

A closed form expression for the evaluation of many-electron matrix elements in the unitary group approach to the theory of atomic structure is presented in terms of simple factors. In addition, a new selection rule for nonvanishing matrix elements is given.

ON A SELECTION RULE FOR ELECTRIC TRANSITIONS IN AXIALLY-SYMMETRIC NUCLEI

2010 ◽  
Vol 19 (04) ◽  
pp. 685-691 ◽  
Author(s):  
A. DOBROWOLSKI ◽  
A. GÓŹDŹ ◽  
J. DUDEK
Keyword(s):  
Transition Matrix ◽  
Selection Rule ◽  
Wave Functions ◽  
Matrix Elements ◽  
Axially Symmetric ◽  
Many Body ◽  
Absolute Value ◽  
Angular Momenta ◽  
Abrupt Changes ◽  
Transition Matrix Elements

We consider many-body E-l transition matrix-elements between two nuclear states of different axially-symmetric deformations characterised by two different (mutually non-orthogonal) sets of single-particle wave-functions. Yet, when varying the deformations of the initial, final, or both these states one notices abrupt changes in the form of vanishing and possibly reappearance of the transition matrix elements calculated between the corresponding Slater determinants. The mechanism is explained in terms of the conservation of the |m| quantum number (absolute value of the projection of individual-nucleonic angular-momenta); consequences for the more general calculations of this type also without axial symmetry are discussed.

GENERALIZED HYPERVIRIAL AND RECURRENCE RELATIONS FOR RADIAL MATRIX ELEMENTS IN ARBITRARY DIMENSIONS

2005 ◽  
Vol 20 (20) ◽  
pp. 1533-1540 ◽  
Author(s):  
SHI-HAI DONG ◽  
M. LOZADA-CASSOU
Keyword(s):  
Recurrence Relation ◽  
Recurrence Relations ◽  
Selection Rule ◽  
Recurrence Formula ◽  
Higher Dimensions ◽  
Wave Functions ◽  
Matrix Elements ◽  
Central Potential ◽  
Isotropic Harmonic Oscillator ◽  
Arbitrary Dimensions

In this letter, based on Hamiltonian identity we propose a generalized expression of the second hypervirial for an arbitrary central potential wave functions in higher dimensions D and then present a useful general recurrence relation among the off-diagonal multipolar matrix elements. We show that this new proposed recurrence formula is very powerful in deriving the recurrence relations among the hydrogenic matrix elements. Some important recurrence relations can be simply obtained. It is interesting to find that the selection rule is independent of the central potential V(r) for f = rk with k = 0, 2 and that the diagonal matrix elements of V′(r) are independent of the system eigenvalues for k = 1. The application of the general recurrence relation to the isotropic harmonic oscillator case is discussed briefly.

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