Empirical evidence for magic numbers of superdeformed shapes

Abstract

We present for the first time many types of empirical evidence that point to the existence of preferred neutron/proton numbers for superdeformed (SD) shapes. We use a simple premise based on the pairing correlations to obtain the proposed empirical evidence. In particular, plots of γ -ray energy ratio such as R(I ) = E γ (I → I -2)/ E γ (I -2 → I -4) vs N and Z, R(I ) vs I plots, nuclear softness parameter values, and the number of SD bands for a given N and Z are used to pinpoint the N , Z numbers that are most favored as the deformed magic numbers. The proton and neutron magic numbers so obtained not only confirm the earlier theoretical predictions made for the chain of particle numbers corresponding to the SD shapes but also verify the increase in deformation with the particle number within each chain. The analysis also leads to several new predictions for the occurrence of the SD bands.

Azimuthal asymmetries in semi-inclusive J/ψ+jet production at an EIC

“…We take z = 0.7, y = 0.3 (left) or z = 0.3, y = 0.7 (right). Two sets of LDMEs are used: SV[46] and CMSWZ[47]. The ratio of the collinear quark contribution over the total unpolarized cross section is shown in the form of a band, representing the scale uncertainty and the results obtained with the two LDME sets, for the center-of-mass energy √ s = 65 GeV.…”

“…Upper bounds for the absolute values of A W , with W = cos 2φT , cos 2(φT − φ ⊥ ) for the Υ, in NRQCD and in the CSM, at Q 2 = 100 GeV 2 , as a function of K ⊥ at y = 0.3 and z = 0.7 (left) and as a function of y at K ⊥ = 4 GeV and z = 0.6 (right). The SV set of LDMEs[46] is used. The ratio of the collinear quark contribution over the total unpolarized cross section is shown in the form of a band, representing the scale uncertainty, for the center-of-mass energy √ s = 65 GeV.…”

Band head spin assignment of Tl isotopes of superdeformed rotational bands

“…The nuclear softness parameter, (σ ), is related to the rigidity of the nucleus and increases with super deformation indicating near rigid rotor behavior. Nuclear softness parameters for SD bands are observed in the range 10 −4 ≤ σ ≤ 10 −6 [29][30][31]. Comparing this range to that of the ND bands [32,33] , shows that the SD bands are much more rigid than the ND bands.…”

Gluon TMDs and NRQCD matrix elements in $${J}{/}{\psi }$$ production at an EIC

“…In the latter case, the pair becomes colorless after the emission of soft gluons. The CS LDMEs are commonly obtained from potential models [36], lattice calculations [37] or from leptonic decays [38], while the CO ones are usually determined by fits to data on J/ψ and Υ yields [39][40][41][42][43], but not from lattice calculations. As a result, at present our knowledge of the CO matrix elements is not very accurate (cf .…”