Extracting the spectral signature of $\ensuremath{\alpha}$ clustering in $^{44,48,52}\mathrm{Ti}$ using a continuous wavelet transform

Rapid Communication

Extracting the spectral signature of $α$ clustering in ${}^{44, 48, 52}{Ti}$ using a continuous wavelet transform

Sam Bailey, Tzany Kokalova, Martin Freer, Carl Wheldon, Robin Smith, Joseph Walshe, Neil Curtis, Neven Soić, Lovro Prepolec, Vedrana Tokić, Francisco Miguel Marqués, Lynda Achouri, Franck Delaunay, Quentin Deshayes, Marian Parlog, Beatriz Fernández-Dominguez, Bertrand Jacquot, and Asim Soylu

Phys. Rev. C 100, 051302(R) – Published 15 November 2019

Abstract

A novel technique has been developed, making use of the continuous wavelet transform to identify $α$ -clustered states from resonant scattering measurements in regions of high nuclear state density. This technique expedites the investigation of $α$ clustering in medium mass and heavy nuclei where the role that $α$ clustering plays in the structure of the nucleus is poorly understood. Here, we report the application of this technique to measurements of the ${}^{4}{He} ({}^{40, 44, 48}{Ca}, α)$ resonant reactions, leading to an assessment of the $α$ -cluster structure of ${}^{44, 48, 52}{Ti}$ . Clustering involving α particles was identified in ${}^{44}{Ti}$ and ${}^{52}{Ti}$ but was observed to break down in ${}^{48}{Ti}$ . The implications of these results are discussed.

Received 10 January 2019

DOI:https://doi.org/10.1103/PhysRevC.100.051302

Physics Subject Headings (PhySH)

Low & intermediate energy heavy-ion reactions Nuclear structure & decays

39 ≤ A ≤ 58

Cluster models Spectrometers & spectroscopic techniques

Nuclear Physics

Authors & Affiliations

Sam Bailey ¹, Tzany Kokalova^1,*, Martin Freer¹, Carl Wheldon¹, Robin Smith^1,†, Joseph Walshe¹, Neil Curtis¹, Neven Soić², Lovro Prepolec², Vedrana Tokić², Francisco Miguel Marqués³, Lynda Achouri³, Franck Delaunay³, Quentin Deshayes³, Marian Parlog^3,4, Beatriz Fernández-Dominguez⁵, Bertrand Jacquot⁶, and Asim Soylu⁷

¹School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, United Kingdom
²Institut Ruđer Bošković, Bijenička cesta 54, 10000 Zagreb, Croatia
³Laboratoire de Physique Corpusculaire de Caen, 6 bd Maréchal Juin, 14050 Caen Cedex, France
⁴“Horia Hulubei” National Institute of Physics and Nuclear Engineering (IFIN-HH), RO-077125 Bucharest Magurele, Romania
⁵Universidade de Santiago de Compostela, Praza do Obradoiro, 15782 Santiago de Compostela, Spain
⁶Grand Accélérateur National d'Ions Lourds, Bd Henri Becquerel, Boîte Postale 55027-14076 Caen Cedex 05, France
⁷Department of Physics, Niğde University, 51240, Niğde, Turkey

^*Corresponding author: t.kokalova@bham.ac.uk
^†Present address: Department of Engineering and Mathematics, Sheffield Hallam University, City Campus, Howard Street, Sheffield, S1 1WB, United Kingdom.

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Vol. 100, Iss. 5 — November 2019

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Figure 1
Measured excitation spectra. (a)–(c) Measurements of the differential cross section, made at a center-of-mass scattering angle of $180^{\circ}$ , of (a) the ${}^{4}{He} ({}^{40}{Ca}, α)$ , (b) ${}^{4}{He} ({}^{44}{Ca}, α)$ , and (c) ${}^{4}{He} ({}^{48}{Ca}, α)$ reactions. The resonances in these measurements are relevant to the structure of ${}^{44}{Ti}, {}^{48}{Ti}$ , and ${}^{52}{Ti}$ respectively.
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Figure 2
The CWTs of the measured spectra. (a)–(c), Spectrograms of (a) the ${}^{4}{He} ({}^{40}{Ca}, α)$ , (b) ${}^{4}{He} ({}^{44}{Ca}, α)$ , and (c) ${}^{4}{He} ({}^{40}{Ca}, α)$ excitation spectra. In each case: measured excitation energy spectrum with the Rutherford contribution subtracted (horizontal spectrum), absolute value of wavelet transform $| W_{Ψ} |$ (lower colored two-dimensional plot) and the wavelet power spectrum $P_{Ψ}$ in arbitrary units (vertical right spectrum). The arrows indicate characteristic energy scales. (d) A comparison of the power spectra for each measurement.
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Figure 3
A schematic of a double humped fission barrier. (a) The application of a double humped fission barrier to fragmented $α$ -clustered states with class-I and class-II states indicated. Adapted from Ref. [25, pp. 97–98]. (b) A schematic $X (α, α)$ cross section resulting from this structure. For simplicity, the Rutherford contribution is not shown.
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Figure 4
A comparison of the CWTs of the simulated spectra with and without coupling to class-II states. (a) and (b) Spectrogram of a single iteration (a) without coupling to class-II states and (b) with coupling to class-II states. (c) and (d) An average over 500 spectrograms (c) without coupling to class-II states and (d) with coupling to class-II states. In all cases, the class-II states were fixed at $E^{(I I)} = 13.5$ , 16, and 18 MeV and $γ_{α}^{(I I) 2} = 0.1 MeV$ . The set of class-I states was defined by $〈 D_{J^{π}}^{(I)} 〉 = 0.15, 〈 γ_{α}^{(I) 2} 〉 = 0.0005$ , and $〈 γ_{μ \neq α}^{(I) 2} 〉 = 0.01 MeV$ . The coupling constant $H_{c} = 0.1 MeV$ .
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Figure 5
CWTs of the measured spectra with an $F_{Ψ}$ analysis. (a) and (b) Spectrograms as in Fig. 2 for (a) ${}^{44}{Ti}$ and (b) ${}^{52}{Ti}$ . The quantity $F_{Ψ}$ is calculated between $S_{min}$ and $S_{max}$ (white lines) and overlaid in red on the spectra. The blue arrows indicate the $α$ -clustered states extracted from this analysis.
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Figure 6
A comparison between the previously measured high-lying $α$ -clustered states in ${}^{44}{Ti}$ and those extracted in the present Rapid Communication. The states extracted in the present Rapid Communication are shown in red, denoted by $P$ . Those measured previously are denoted by $E$ , and theoretical energy levels predicted by an $α$ -cluster model are denoted by $T$ . States that have been observed previously as groups of fragmented states are shown as three lines. This figure is adapted from Fig. 29 in Ref. [4, Chap. 2], and both the previously measured and the theoretically predicted energy levels are taken from that work.
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Physical Review C

covering nuclear physics

Extracting the spectral signature of $α$ clustering in ${}^{44, 48, 52}{Ti}$ using a continuous wavelet transform

Sam Bailey, Tzany Kokalova, Martin Freer, Carl Wheldon, Robin Smith, Joseph Walshe, Neil Curtis, Neven Soić, Lovro Prepolec, Vedrana Tokić, Francisco Miguel Marqués, Lynda Achouri, Franck Delaunay, Quentin Deshayes, Marian Parlog, Beatriz Fernández-Dominguez, Bertrand Jacquot, and Asim Soylu

Phys. Rev. C 100, 051302(R) – Published 15 November 2019

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Physical Review C

covering nuclear physics

Extracting the spectral signature of α clustering in Ti44,48,52 using a continuous wavelet transform

Sam Bailey, Tzany Kokalova, Martin Freer, Carl Wheldon, Robin Smith, Joseph Walshe, Neil Curtis, Neven Soić, Lovro Prepolec, Vedrana Tokić, Francisco Miguel Marqués, Lynda Achouri, Franck Delaunay, Quentin Deshayes, Marian Parlog, Beatriz Fernández-Dominguez, Bertrand Jacquot, and Asim Soylu

Phys. Rev. C 100, 051302(R) – Published 15 November 2019

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Extracting the spectral signature of $α$ clustering in ${}^{44, 48, 52}{Ti}$ using a continuous wavelet transform