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Assuming spins of 3/2, 5/2, 7/2 for Zr 91 , the expected ratios are 2.3±0.2, 1.00d=0.07, 0.56zb0.04, respectively, according to the formulawhere #\ is the amplitude of the rf field, m the concentration of the nuclei, and y the gyromagnetic ratio. The experimentally determined ratio of the signals is therefore compatible with a spin 5/2 for Zr 91 as measured by Arroe and Mack.Using the ratio of the magnetic moments of H 1 and D 2 as determined by Smaller, 4 At (H 1 )/M(D 2 ) = 3.2571999d=0.0000012, and the value of the proton magnetic moment, 5 M(H 1 ) = 2.79275±0.00003 nm, the diamagnetically uncorrected value of the magnetic moment of Zr 91 can be calculated as M (Zr 91 ) = -1.29802±0.00002 nm, or, diamagnetically corrected, as /x(Zr 91 )= -1.30284±0.00002 nm.When one considers the proton number Z = 40 and the neutron number iV=51 (magic plus one), the spin and sign of the magnetic moment are in agreement with the predictions of the simple single-particle model which places the neutron in a d b / 2 state. The deviation of the magnetic moment of 32% from the Schmidt value ju(Sch)= -1.913 nm, however, is rather large. For this reason one may consider configurations which also include protons, particularly the last two protons outside the closed shell Z=28. In terms of the independent-particle model, the two protons would couple their individual spins j p to a total proton spin J p = 0, 2, or 4, whereas J p would couple with the odd-neutron spin y n =5/2, to the total angular momentum /(Zr 91 ) = 5/2. Possible configurations consistent with the exclusion principle are \jr(pi /2 ) 2 J P =o; vdy. 2~] r>/2, L^igviYjp-o; vd bri~]hl2 , \jr(g9/2) 2 J P -2', vd m~] s/2, and [^(^9/2)^^4; vd h( i~] m , which yield the magnetic moments in nuclear magnetons of -1.913, -1.913, +0.037, and +4.04, respectively. This shows clearly that the ground state of Zr 91 cannot be described by one single configuration of the type mentioned.The observed relaxation time 7\ of Zr 91 in aqueous solution of (ZrF 6 ) is of the order of 10~3 sec and indicates an appreciable electric quadrupole moment.

We study systematically the equal-time relativistic equation with a confinement potential, its boundary conditions, and the resulting bag-type solutions and eigenvalues. We show that the flux is continuous across the bag boundary. The chiral symmetry of the equation for vanishing quark masses is spontaneously broken for J = 0 states because of the boundary condition. We'take a model potential consisting of a linear potential and a modified Coulomb potential that vanishes at the origin and show that the Ngmbu-Goldstone condition on the a meson can be implemented, and that the known I = 1 meson spectrum can be accounted for with remarkable success, provided the Coulomb coupling constant g is chosen above the critical value 2.

We clearly also have the restriction \-M u which determines which of the helicity amplitudes of the PI,PQ system survives at t t -0. 13 If the sum over J 2 i n (9) is dominated by a single resonance of spin S 2 , thenMj ^m.ixi(JQ+j it S 2 +J2).The scalar, pseudoscalar, vector, and axial-vector form factors of the pion are derived from (i) the Veneziano amplitudes for 7r + 7r"" -* 7r + 7r"" and 7r + 7r~--*.A 1 + 7r~, (ii) the hypothesis of the partially conserved axial-vector current, and (iii) the requirement that a chirally conjugate pair of form factors should exhibit similar structures. The resulting form factors feature an infinite sequence of poles corresponding to daughters of specific spin and parity, and definite signature. Various predictions on the clashing-beam production of 27r and on p-meson coupling constants are given.Recently, the Veneziano-type form factors for the pion have been discussed by several authors, 1 but these fail to satisfy a natural requirement that a chirally conjugate pair of sources, like the vector current V u a and the axial-vector current A M a , should couple in more or less symmetric ways to an infinite number of particles with specific spin and parity, whose existence is one consequence of the Veneziano model. 2 To illustrate our point, let us take for example the following off-shell TITT scattering amplitude which is consistent with the condition of partially conserved axial-vector current (PCAC) and which reduces to the Veneziano-Lovelace 3 amplitude on the mass shell:(7 r -(g')l9 X A x ( -, (0)k + (/,) )1 r-(g)) = V2/,m" 2 (fe 2 -m ¥ 2 )-1^11 ' 1 (s,awhere B k iJ {s,t)^T{i-a s )T{j-a t )/T{k-a s -a t ).Here k is the momentum of the off-shell n + meson and s = (p + q) 2 , t = (k-p) 2 , and u = (q-k) 2 . a s = a(s) represents the degenerate p-/trajectory and is given by a(s) = | + 6(s-m 7r 2 ) with b~x = 2(m p 2 -m 1T 2 ). A is the pion decay constant and 0o = £>7r7r 2 « Now by continuing to />-0 by means of the standard soft-pion technique the left-hand side of (1) reduces to the pion matrix element of the so-called £ term, t -k 2 , and using a {m ff 2 ) = \ we obtain 4(2)in order to obtain the above normalization. Thus, in spite of our original assumption expressed in (1), namely, that the pseudoscalar source d x A x {mm) (^) couples only to the IT meson, we obtain the result that its chiral counterpart 2 couples to all 0 + daughters of the p-/trajectory. We consider this asym-U 0 <+, W,9^X ( _> (0)]x 0 -0 = 2i6 3

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