Download Advances in Nuclear Physics: Volume 13 by A. W. Thomas (auth.), J. W. Negele, Erich Vogt (eds.) PDF

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browse this site By A. W. Thomas (auth.), J. W. Negele, Erich Vogt (eds.)

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For example, if one uses harmonie oscillator wave functions the removal of the spurious motion of the center of mass reduces the value of the squared charge radius by a factor of i. m. corrections should be extremely important for the bag model. m. 4. Here we are concerned with the effect on observables associated with the bag. 2 we discuss the ambiguities which do not arise in the nuclear case. 1. m. corrections to observables began with the work of Donoghue and Johnson (DJ 80). These authors attempted to calculate the pion decay constant (f) in the bag model.

It can be obtained simply by inverting Eq. 39) to obtain I b, 17) = W(p) (2n)-3 ~(F) f . 42) and substituting into Eq. 43) will, of course, only receive contributions when r is less than twice the bag radius. Having constructed an eigenstate of momentum we can now caIculate any matrix element required. 45) 36 A. W. ) Carlson and Chachkhunashvili (CC 81) exp1icit1y calcu1ated the correction to the naive bag model predictions for the charge radius, magnetic moment, and axial charge using this approach.

45). 46) If we now consider the case where q is infinitesimal, Eq. 48) 48 A. W. Thomas It is a simple exercise to show that Eq. 47) implies that a 2 + 7]:2 is invariant under this chiral transformation. That is, we are merely making a rotation in a four-dimensional (40) space. We mentioned above that under the familiar SU(2) of isospin, a is a scalar and 7]: a vector. 49) a; and [recall Eq. 49) also leaves a 2 + 7]:2 constant. Thus, the most general transformation under SU(2) X SU(2) involves two parameters (q,~) and amounts to nothing more than a rotation in 40 space.

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