Black sphere model for the absorption of negative hadrons by nuclei

Pilkuhn, H.

doi:10.1007/bf01410007

Cited by 3 publications

(1 citation statement)

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“…Since the giant dipole resonance dominates this regime, we have taken L to be one. The probability that a muon will excite the nucleus by this mechanism as it slows through the energy region E 2 to E 1 is given by [8] E2…”

Section: X=ar3l(l+i) L[(2l_i)!!/4~q2(kr)_2l 1 [; Tls*~b(r/r)-l+~ Drmentioning

confidence: 99%

Nuclear excitation via free-bound muon atomic transitions

Kaufmann

Pilkuhn

1977

Z Physik A

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We have examined the probability of the excitation of the giant nuclear dipole resonance through the radiationless capture of a free muon into a bound orbit. Our calculation predicts that the probability is extremely small, about 4 x 10-5 per stopping muon in lead in the surface transition model.A highly excited muonic atom cascades to the ls level rapidly, its excess energy usually being carried off by Auger electrons or by X rays. A third channel for energy release, the transfer of energy directly to the nucleus, has also long been known [1]. For a heavy nucleus such as Bi or Pb approximately 7 % of the stopped muons excite the nucleus. With the intense and very pure muon beams at SIN and LAMPF one may hope to observe direct nuclear excitation from muons captured into bound orbits directly from the continuum, i.e. in flight. This provides information about the nuclear transition charge density of a type different from that available from photoabsorption or gamma decay and in an energy regime different from that explored in the boundbound transitions previously considered 9 We have carried out a study of such nuclear excitation caused by a beam of slowing muons. Because of its great strength we have used the giant dipole resonance as the nuclear level excited. Unfortunately, even for Pb the process is very unlikely 9 On the basis of a surface transition model we find about 4 x 10-5 processes per muon slowing from above the resonance to 0.25 MeV kinetic energy. In the following we discuss the calculational details and give the results and experimental possibilities. The incident muon (velocity v, momentum p~) is assumed captured into the ls bound level. The cross section for the process is found from [-2] where PN is the density of final nuclear states evaluated at the final nuclear excitation energy, the normalization volume for the incident muon is unity, and H' is the Hamiltonian for the interaction between the muon and the nucleus. In the nonrelativistic limit we can ignore the current-current part of the interaction, and assumep, is the nuclear, and pe the muon, transition charge density; these are to be given in Equations (4) and (5). The use of nonrelativistic dynamics is justified on the grounds that: 1) for the case in which the giant resonances are excited the incident muon has kinetic energy of less than about 10 MeV,.which is small compared to the muon rest mass of 105.6 MeV, and 2) even for the tightly bound ls state the small components of the Dirac wave function are only 10 % to 20% of the large components. This gives an indication of the error we are making by use of nonrelativistic dynamics and is quite acceptible for an exploratory calculation of this type. 0

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Section: X=ar3l(l+i) L[(2l_i)!!/4~q2(kr)_2l 1 [; Tls*~b(r/r)-l+~ Drmentioning

confidence: 99%