Existence of higher nodal band states withα+Ca48cluster structure inTi52

Abstract

It is shown that recently observed α cluster states a few MeV above the α threshold energy in 52 Ti correspond to the higher nodal band states with the α+ 48 Ca cluster structure, i.e. a vibrational mode in which the intercluster relative motion is excited. The existence of the higher nodal states in the 48 Ca core region in addition to the well-known higher nodal states in 20 Ne and 44 Ti reinforces the importance of the concept of vibrational motion due to clustering even in medium-weight nuclei with a jj-shell closed core. The higher nodal band and the shell-like ground band in 52 Ti are described in a unified way by a Luneburg lens-like deep local potential due to the Pauli principle, which explains the emergence of backward angle anomaly (anomalous large angle scattering (ALAS)) at low energies, prerainbows at intermediate energies and nuclear rainbows at high energies in α+ 48 Ca scattering. The existence of a K = 0 − α cluster band analog to 44 Ti midway between the ground band and the higher nodal band is inevitably predicted.The α clustering is essential in the 0p-shell and sd shell region and the nuclear structure has been comprehensively understood from the α cluster viewpoint [1]. In the f p shell region, identification of the higher nodal band states with the α+ 40 Ca cluster structure in the fusion excitation functions [2] lead to the prediction of a K = 0 − band, which is a parity-doublet partner of the ground band, in the typical nucleus 44 Ti [3-5]. The observation of the K = 0 − band in experiment [6,7] showed that the α cluster picture is also essential in 44 Ti. Systematic theoretical and experimental studies in the 44 Ti region [8][9][10][11][12][13] confirmed the existence of the α cluster in the beginning of the f p-shell above the double magic nucleus 40 Ca.α clustering aspects in nuclei beyond 44 Ti have been explored in the medium weight mass region around A=50 such as 48 Cr [14,15] and 46,50 Cr [16,17] as well as in the heavy mass region such as 94 Mo and 212 Po [18][19][20][21]. 52 Ti, which is a typical nucleus with two protons and two neutrons outside the doubly closed core 48 Ca analog to 20 Ne and 44 Ti, has been mostly studied in the shell model [22][23][24][25][26][27]. The ground band 0 + , 2 + and 4 + states are selectively enhanced in the α-transfer reactions such as 48 Ca( 16 O, 12 C) 52 Ti [28] and 48 Ca( 12 C, 8 Be) 52 Ti [29]. However a microscopic α+ 48 Ca cluster model calculation with Brink-Boeker force B1 using the generator coordinate method (GCM) [30] did not give the ground band as well as in the α+ 40 Ca cluster model calculation for 44 Ti. On the other hand, Ohkubo et al. [31] and Ohkubo and Hiraoka[32] reproduced the ground band of 52 Ti in the α cluster model with a local potential similar to 44 Ti [3, 4]. No experimental data that suggest clear α cluster states hampered to conclude that the α cluster picture persists in 52 Ti in the jj-shell closed 48 Ca core region. Very recently Bailey et al.[33] reported that they newly observed α cluster states at the highl...

Search for the $α$ + core structure in the ground state bands of $22 \leq Z \leq 42$ even-even nuclei

“…In the case of 52 Ti, the α+ 48 Ca potential of this work produces E x (1 − ) = 7.842 MeV for the G = 13 band. This value is above that predicted by Ohkubo [16] (E x (1 − ) = 6.90 MeV ), which uses a Woods-Saxon squared local potential for the α + core nuclear interaction. The α + core nuclear potential of Ref.…”

“…In the last decades, α-clustering has been analyzed by LPM in several studies emphasizing the nuclei with the α + {doubly closed shell core} (hereafter: α + DCSC) configuration, such as 20 Ne, 44 Ti, 52 Ti, 60 Zn, 94 Mo, and 212 Po (examples in Refs. [5][6][7][8][9][10][11][12][13][14][15][16][17][18]). In this way, some works demonstrate that the nuclei with the α + DCSC configuration can be systematically analyzed with the same α + core potential type, providing a good general agreement with experimental data, as shown in Refs.…”

“…In recent years, the Ti isotopes have been investigated theoretically and experimentally from the perspective of the α-cluster structure [16,[23][24][25]. In the studies of S. Bailey et al [23,24], a novel technique makes use of the continuous wavelet transform and machine learning to identify α-clustered states in 44,48,52 Ti through 4 He( 40,44,48 Ca, α) resonant scattering measurements; such studies indicate the presence of the α+ 40 Ca and α+ 48 Ca structures in high-lying states of 44 Ti and 52 Ti, respectively.…”

“…The results of S. Bailey et al reinforce the indications of previous experiments which also point to the presence of the α-cluster structure in Ti isotopes, as the 40,42,48 Ca( 6 Li, d) 44,46,52 Ti [26][27][28][29][30] and 40,42 Ca( 7 Li, tα) 40,42 Ca [31] reactions, and other α-transfer processes on Ca targets. The work of S. Ohkubo [16] discusses the α+ 48 Ca structure in 52 Ti, using the optical potential model to analyze α+ 48 Ca scattering data; the real part of the optical potential was used to calculate the α+ 48 Ca energy bands, indicating that three 52 Ti experimental states found by S. Bailey et al [23] are associated with the higher nodal positive parity band of the α+ 48 Ca system.…”

Yrast band in the heavy N = Z nucleus $$^{88}$$Ru: $$\alpha $$-cluster approach

“…the recent review [9]), and 94 Mo = 90 Zr ⊗ α was often used to fill the wide gap of missing stable doubly-magic core nuclei between A ≈ 40 and A > 200 [11]. In this gap, the α-decay in the N = Z system 104 Te = 100 Sn ⊗ α was also under study very recently [12][13][14][15][16], and 52 Ti = 48 Ca ⊗ α was investigated in [17]. A detailed introduction into the nuclear cluster model is provided in a dedicated special issue of [18][19][20][21][22][23][24][25].…”