scholarly journals The identification of $${{\varvec{\alpha }}}$$-clustered doorway states in $$^{44,48,52}$$Ti using machine learning

2021 ◽  
Vol 57 (3) ◽  
Author(s):  
Sam Bailey ◽  
Tzany Kokalova ◽  
Martin Freer ◽  
Carl Wheldon ◽  
Robin Smith ◽  
...  

AbstractA novel experimental analysis method has been developed, making use of the continuous wavelet transform and machine learning to rapidly identify $$\alpha $$ α -clustering in nuclei in regions of high nuclear state density. This technique was applied to resonant scattering measurements of the $$^\text {4}$$ 4 He($$^\text {40,44,48}$$ 40,44,48 Ca,$$\alpha $$ α ) resonant reactions, allowing the $$\alpha $$ α -cluster structure of $$^\text {44,48,52}$$ 44,48,52 Ti to be investigated. Fragmented $$\alpha $$ α -clustering was identified in $$^\text {44}$$ 44 Ti and $$^\text {52}$$ 52 Ti, while the results for $$^\text {48}$$ 48 Ti were less conclusive, but suggest no such clustering.

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1106
Author(s):  
Jagdish N. Pandey

We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).


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