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Download Advances in Nuclear Physics: Volume 4 by Daphne F. Jackson (auth.), Michel Baranger, Erich Vogt PDF

By Daphne F. Jackson (auth.), Michel Baranger, Erich Vogt (eds.)

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Extra info for Advances in Nuclear Physics: Volume 4

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Phys. A12S:1 (1969). ] 3 5 7 R(fm) II 20 Daphne ~ Jackson term containing the nuclear structure information (the spectroscopic factor) and a term depending on the reaction mechanism. This leads to the possibility of obtaining additional nuclear structure information which is discussed in Section 4. 4. , is such that the analyses are usually restricted to the removal of nucleons in the same shell and the overlap integrals are usually constructed from oscillator functions (Bay 64). Some progress has recently been made (Rot 69) in deriving spectroscopic factors for these reactions using an oscillator basis and the generalization of the Brody-Moshinsky transformation brackets due to Smirnov (Smi 61, Smi 62).

The angle Om is shifted slightly by distortion and relativistic corrections to the energies. The first integral in Eq. (31) can be rewritten in the form (39) where i(po + Q), i(Pl - P2) are the momenta of the scattered proton before and after collision in the proton-proton center of mass system. Using impulse approximation 1 Tpp 12 can be formally expressed in terms of the free proton-proton cross section, (BJ 63, MHR 58) but because of the energy required to release the bound proton the matrix element Tpp is off the energy-shell for free p-p scattering.

1). Now using Eq. (3), we have G(Q) = = L CrzfJf I t/>~*(r)t/>,/'(r) dr I i rzfJ L CrzfJfP(a,k)GP(Q) 'l'fi Q · R v4B(R) is the overlap dR (52a) (52b) rz{J where pea, k) is defined by Eq. (19a) and G(Q) by Eq. (23) and, if complete overlap of the wave functions of the free deuteron and deuteron cluster is assumed so that pea, k) is given by Eq. (19b), Eq. (52) reduces to G(Q) = L C1ePIGfJ(Q) fJ (53) Hence in the quasi-free model the dependence of the cross section on the recoil momentum Q gives information about the momentum components of the reduced overlap integral defined in Eq.

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