Hypernuclear physics with pions

We investigate the possibility of producing hypernuclei with energetic pion beams via the (π⁺, K⁺) reaction. Due to the high momentum transfer involved (q≈300 MeV/c), even in the forward direction, the (π⁺, K⁺) reaction preferentially populates high spin natural parity configurations obtained by coupling a Λ particle to a neutron hole. We present differential cross section calculations utilizing the plane wave approximation (PWA), the distorted wave impulse approximation (DWIA) using fully distorted waves, and the eikonal approximation (EIK) to approximate distortion effects. The DWIA and EIK results are in agreement, and lead to cross sections typically a factor of 5-10 lower than the PWA results, due to absorptive effects. Cross sections of 5-20 {μ}b/sr at 0^∘{} are obtained in the DWIA for high spin natural parity "stretched configurations," for example (_Λd3/2,5/2ₙf7/2^-1)^5_- or (_Λf5/2,7/2ₙf7/2^-1)^6₊ in _Λ⁴⁸Ca, for pion lab momentum p_π in the range 1.02-1.1 GeV/c, where the elementary cross section for K⁺n→π⁺Λ has its peak values. The cross sections for the population of the natural parity ground-state levels (_ΛS1/2ₙll+1/2^-1)J=l with closed shell targets remain above 2 {μ}b/sr at 0^∘{} for systems lighter than A≈50. The cross sections drop rapidly below p_π=1.02 GeV/c, due to threshold effects. Results are presented for the calculated quasielastic (quasifree) continuum background for the (π⁺, K⁺) reaction as a function of θ1ab and hypernuclear excitation energy. Because of the higher momentum transfer the quasielastic background is broader and significantly less in magnitude than that obtained in the (K^-, π^-) reaction at 0^∘{}. Thus it should be possible to measure cross sections of a few {μ}b/sr associated with particle-hole states using existing pion beams in the 1-1.5 GeV/c momentum range, for instance at the Brookhaven AGS. The class of hypernuclear states populated at 0^∘{} in a (π⁺, K⁺) reaction is complementary to those seen in the "crossed" (K^-, π^-) reaction at 0^∘{}, the latter being sensitive only to low spin states. Thus the (π⁺, K⁺) reaction offers unique possibilities for extending our knowledge of hypernuclear structure.NUCLEAR STRUCTURE Excitation of high spin states in (π, K) reaction. DWIA and PWA estimates of cross sections.