A spectroscopic analysis of mesons is carried out within the framework of the harmonic-oscillator quark model, in which the configuration mixing of radially excited harmonic-oscillator states in meson wave functions is considered. The first radially excited state of the .rr meson is predicted at 1370 MeV, which could be a ST resonance. The recently observed p'(i500) resonance bump is speculated to consist of a radially excited state of the p meson at 1530 MeV and an orbitally excited state at 1410 MeV. The long-observed E(1420) and o (1675) are identified as the first radially excited states of the 7 and I $ mesons, respectively.In this note we shall r e p o r t a consistent analysis of the meson m a s s spectrum within the nonrelativistic harmonic-oscillator quark model. In the SU(6) x O(3) classification scheme,' a l l the radially excited harmonic-oscillator s t a t e s a r e ignored. However, if the supermultiplet s t r u c t u r e of the meson m a s s spectrum does come f r o m a s u p e rstrong harmonic -oscillator well, the complete s e t of the harmonic-oscillator s t a t e s should b e taken in the dynamical calculation of the m a s s levels. Hence the existence of radially excited mesons m u s t be taken into s e r i o u s consideration. in fact, t h e r e has been speculation of the well-established E(1420) meson being a radially excited state of the q ( o r 7 ' ) meson after a proper S1J(6)x0(3) assignment w a s not successfully made.'In our analysis we a s s u m e that the wave function of a meson of spin parity J P and SU(3) label y i s written a s a linear combination of the radial-excitation harmonic-oscillator s t a t e s (labeled by . zs+ LL, , . n = principal quantum number, S = q u a r k spin? L =angular momentum),n where n = O , 1 , 2 , . . . . In practical computation the s e r i e s (1) t e r m i n a t e s a t n =n,,,.The m a s s operator i s assumed to be where A is equivalent to twice the effective m a s s of a quark in the mesons; N = 2 n + L i s the number of quantum excitation; w is the harmonic-oscillator quantum energy; and V ( v ) is the residual potential between two constituent q u a r k s , which we a s s u m e to b e a Gaussian well, viz., f o r singlet spin s t a t e s , and for triplet spin states. Assuming only the spinspin and the spin-orbit interactions in the potential V(V), we have where the well depths I; a r e SU(3)-dependent. In the following, the SU(3) label y will be denoted by [dim SU(3), 21+ 11, 1 being isospin. Consider f i r s t the isotriplet mesons. The m a s s values of the eight well-established mesons,3 n(140) IS,, B(1235) 'P,, A3(1640) I D , , p(770) 3S,, 6(970) 3P,, A1(llOO) ' P I , Az(13f0) 3P2, F1(1540) 3~2 , and g(1680) '~3 , determine the potential p a r a m et e r s , A , w , u,SS<8,3), u s S ( 8 , 3 ) , !7f0(8,3), O,, and p,, by a l e a s t -s q u a r e s fit to the lowest eigenvalues of the m a s s operator (2). The r e s u l t s a r e given in Table I f o r the c a s e s n,,,=O, 1, and 2. It i s s e e n that an i n c r e a s e in the number of radi...
The g factor of the '-~s tate in Sc is discussed within the framework of the conventional shell model. An inert Ca core is assumed. The effective interaction derived for this mass region by Kuo and Brown is used. It is shown that the g factor can be well explained with a small configuration mixing. The g factor of the 6+ state in Ca is also discussed.The explanation of the measured magnetic dipole moments provides a useful probe in the study of nuclear structure. %'ith the j-j coupling shell model, the various features of the deviations of magnetic dipole moments from the Schmidt values were interpreted by configuration mixing for almost the whole region of nuclei. ' Freed and Kisslinger' carried out the calculations using the same method, but within the framework of the pairing model. For the magnetic dipole moments of p,~, -shell nuclei, the importance of the tensor force which causes the configuration mixing is emphasized in the explanation of the small deviations from the Schmidt values. ' However, these calculations were restricted to the magnetic dipole moments of the ground state of odd-mass nuclei, where the mixed senioritythree configurations were assumed to be the initial nucleon of the seniority-one configuration coupled to the other two nucleons of the same kind having equal orbital angular momenta and J = 1.The deviations from the Schmidt values of the magnetic dipole moments of high-spin excited states have been studied in the '"Pb region' and A = 88 region. ' The anomalous g'" factor of about
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