Examination of evidence for collinear cluster tri-partition

Background: In a series of experiments at different time-of-flight spectrometers of heavy ions we have observed manifestations of a new at least ternary decay channel of low excited heavy nuclei. Due to specific features of the effect, it was called collinear cluster tri-partition (CCT). The obtained experimental results have initiated a number of theoretical articles dedicated to different aspects of the CCT. Special attention was paid to kinematics constraints and stability of collinearity.

Purpose: To compare theoretical predictions with our experimental data, only partially published so far. To develop the model of one of the most populated CCT modes that gives rise to the so-called “Ni-bump.”

Method: The fission events under analysis form regular two-dimensional linear structures in the mass correlation distributions of the fission fragments. The structures were revealed both at a highly statistically reliable level but on the background substrate, and at the low statistics in almost noiseless distribution. The structures are bounded by the known magic fragments and were reproduced at different spectrometers. All this provides high reliability of our experimental findings. The model of the CCT proposed here is based on theoretical results, published recently, and the detailed analysis of all available experimental data.

Results: Under our model, the CCT mode giving rise to the Ni bump occurs as a two-stage breakup of the initial three body chain like the nuclear configuration with an elongated central cluster. After the first scission at the touching point with one of the side clusters, the predominantly heavier one, the deformation energy of the central cluster allows the emission of up to four neutrons flying apart isotropically. The heavy side cluster and a dinuclear system, consisting of the light side cluster and the central one, relaxed to a less elongated shape, are accelerated in the mutual Coulomb field. The “tip” of the dinuclear system at the moment of its rupture faces the heavy fragment or the opposite direction due to a single turn of the system around its center of gravity.

Conclusions: Additional experimental information regarding the energies of the CCT partners and the proposed model of the process respond to criticisms concerning the kinematic constraints and the stability of collinearity in the CCT. The octupole deformed system formed after the first scission is oriented along the fission axis, and its rupture occurs predominantly after the full acceleration. Noncollinear true ternary fission and far asymmetric binary fission, observed earlier, appear to be the special cases of the decay of the prescission configuration leading to the CCT.

Detection of the ${}^{68–72}\mathrm{Ni}$ fission fragments with a kinetic energy $E<25\mathrm{MeV}$ at the mass-separator Lohengrin is proposed for an independent experimental verification of the CCT.

Figure 1

(a) Ex1: contour map (in logarithmic scale, the steps between the lines are approximately factor 2.5) of the mass-mass distribution of the collinear fragments of ${}^{252}\mathrm{Cf}\left(sf\right)$, detected in coincidence in the two opposite arms of the FOBOS spectrometer. The arrow marks a specific bump in arm1. (b) Projection of the Ni bump onto $M_1$ axis obtained in three different experiments performed at the FOBOS spectrometer modules. It should be noted that (a) was published in Ref. [1] and (b) in Ref. [2].

Figure 2

Ex3: region of the mass-mass distribution for the FFs from ${}^{252}\mathrm{Cf}\left(sf\right)$ around the Ni bump [similar to that marked by an arrow in Fig. 1]. It should be noted that (b) was published in Ref. [2].

Figure 3

Ex3: velocities $V$ and energies $E$ for the ternary events with $M_L=\left(67–75\right)\mathrm{u}$ [Ni peaks in Fig. 2]. Correlation between the velocities of two lighter partners of the ternary decay (a); energy spectrum of the detected Ni nuclei (the yields per binary fission are marked above each peak) (b); energy correlations $E_L–E_T$ and $E_L–E_H$ (c) and (d) respectively. The sketches in the panels illustrate the decay scenario to be discussed below. See the text for details.

Figure 4

Ex3: the spectrum of excitation energy in the scission point $E_{\mathrm{ex}}=Q_3–\mathrm{TK}{\mathrm{E}}_3$ for the events presented in Fig. 3.

Figure 5

Ex2: (a) results for experimental neutron multiplicity, $n=2$, the mass-mass distribution of the FFs, and an additional gate in the $V_1–E_1$ plot [2]. The lines are drawn to guide the eye. (b) Energy $E_1$ for ${}^{68,72}\mathrm{Ni}$ nuclei [marked by arrows 1 and 2 in (a)]. It should be noted that Fig. 5 was published in Ref. [2]. See the text for more details.

Figure 6

Macroscopic potential energy (dashed line), shell correction (dotted line), and total macro-microscopic potential energy (solid line) of the ${}^{252}\mathrm{Cf}$ nucleus corresponding to the ${}^{132}\mathrm{Sn}{+}^{48}\mathrm{Ca}{+}^{72}\mathrm{Ni}$ ternary splitting [6]. Here $R$ is an approximate distance between the mass centers of the side fragments, $R_0=1.16A^{1/3}$ is a radius of a mother nucleus.

Figure 7

The potential energy $V$($R_{12},x3,y3=0$) of the TNS as a function of $x3$ at different values of $R_{12}=19$, 20, 21, 22, 23 fm. Inset: the scheme showing the variables used in the calculation [10] of the potential energy $V$($R_{12},x3,y3$) (a). The same is true for the $R_{12}=26,27,28$ fm (b). The potential energy surface $V$($R_{12},x3,y3$) as a function of the position $x3$ and $y3$ of the center-of-mass of the middle fragment “3” (Ca) at the value of $R_{12}=21\mathrm{fm}$ (the relative distance between centers of fragments’ masses “1” and “2”) (c) and of $R_{12}=24\mathrm{fm}$ (d).

Figure 8

Areas of attainable final fragment kinetic energies vs the excitation energy of the intermediate fragment in the sequential decay ${}^{252}\mathrm{Cf}\left(sf\right)\to \mathrm{Sn}+\mathrm{Cd}\to \mathrm{Sn}+\mathrm{Ca}+\mathrm{Ni}$. The colors indicate formation position, as shown by the inset (a). Similar graphs but for the true ternary decay ${}^{252}\mathrm{Cf}\left(sf\right)\to \mathrm{Sn}+\mathrm{Ca}+\mathrm{Ni}$. Each figure is a specific element, and different areas indicate the choice of $x_r$, as shown in the upper part of the figure (b). Contact position of the TP with LF corresponds to $x_r=1$ (appropriate regions are shown in black) [5].

Figure 9

Pictograms illustrating scenarios of different CCT modes observed in the experiment. See the text for details.

Figure 10

Velocities $V_L,V_T$ and energy $E_H$ of the ternary fragments satisfying the system (1). Calculations were performed for the locus $w3b$. See text for details.

Figure 11

Potential energy of a fissioning ${}^{252}\mathrm{Cf}$ nucleus, corresponding to the bottoms of the potential valleys, as a function of $Q$, proportional to its quadrupole moment. The valleys found are marked by numbers 1–5. The panels depict the shapes of the system at the points marked by arrows (a). The conditional experimental mass-energy distribution $P\left(M\right|E^{*})$, where $E^{*}$ is an excitation energy at the scission point. The panels depict the shapes of the fissioning system following from the calculations ascribed to the two dominant structures [39] (b).

Figure 12

Partial fragment mass distributions for fixed numbers of emitted neutrons for ${}^{252}\mathrm{Cf}$ (a),(b), ${\nu }_L/{\nu }_H$ denotes the number of neutrons emitted from the light and heavy fragments, respectively. The yield is normalized to the total number of events with the neutron multiplicity ${\nu }_{\mathrm{tot}}={\nu }_L+{\nu }_H$ [40].

Figure 13

Energy spectrum of ${}^{252}\mathrm{Cf}$ ternary fission events, measured with a low-energy threshold of 25 MeV. The inset indicates the corresponding mean angles (a). Mass distribution calculated from the measured energies and angles using momentum conservation [49] (b).

Figure 14

Absolute fragment-mass yields for the reactions induced by thermal neutrons [57].