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Nuclear charge distribution in the spontaneous fission of 252Cf

The measurement for charge distributions of fragments in 252Cf has been performed by using a unique style of detector setup consisting of a typical grid ionization chamber and a dE-E particle telescope. We found that the fragment mass dependency of the average width of the charge distribution shows a systematic decreased trend with the obvious odd-even effect. The variation of widths of charge distribution with kinetic energies shows an approximate V-shape curve due to the large number of neutron emission for the high excitation energies and cold fragmentation with low excitation energies. As for the behavior of the average nuclear charge with respect to its deviation {\Delta}Z from the unchanged charge distribution (UCD) as a function of the mass number of primary fragments A*, for asymmetric fission products {\Delta}Z is negative value, while upon approaching mass symmetry {\Delta}Z turns positive. Concerning the energy dependence of the most probable charge for given primary mass number A*, the obvious increasing tendencies for with the kinetic energies are observed. The correlation between the average nuclear charge and the primary mass number is given as linear function. The proton and neutron odd-even effects with light fragment kinetic energies are derived.


Introduction
The nuclear fission reaction is a complex process involved by the nuclear dynamics in which a rearrangement of nuclear matter takes place during the descent from the saddle point to the scission. The investigations of the mass, nuclear charge and kinetic energy distributions of fragments as well as observations of correlations between these physical quantities not only can provide valuable information for understanding the probability of coupling collective modes to particle excitation degrees of freedom but also contribute to explore the delicate interplay between the macroscopic aspects of bulk nuclear matter and the quantum effects of a finite nuclear system. Up to present the mass and kinetic energy distribution of fragments have been Besides the radiochemical method with the shortcoming of depending on the data of nucleus decay diagram [1], several physical approaches, such as K x-ray intensities in coincidence with fragments [2], the energy loss of mass separated fragments in the absorber [3], ∆Ε−Ε particle telescope in coincidence with K x-ray detector [4,5], the gravity of the electron-ion pair track produced by fragments [6,7], the prompt γ-ray in coincidence with fragments [8] and the γ-γ coincident measurement with Gammasphere [9] could be employed to determined the nuclear charge of fragments in fission reactions. It was found from checking the experimental data up to today that the charge distributions of fragments at the selected excitation energies and mass numbers in the cold region of the spontaneous fission of 252 Cf have been shown by Knitter et al. [6]. However, probably the best way for investigating charge distributions of fragments is via the mass-spectrometer associated with the fragment residual energy detection [3,10] or with the ∆Ε−Ε ionization [11], since the nuclear charge resolution of Z/∆Z~40 was obtained and the variation of the charge distribution with mass numbers and kinetic energy of fragments in a wide mass region could be given by using this method [3].
A new technique employed in the present work, namely, a typical grid-ionization chamber coupled with a ∆Ε−Ε particle telescope [12] multiplicities is employed in the data analysis procedure. As for nuclear charge distribution, the approach employed in Ref. [6] is that they exploited Z dependence of quantity X which is the distance of the centre of gravity of the electron-ion pair track from the origin of the trace, and is in general a function of fragment energy E, mass A, and charge Z. The distributions of charge dependent quantity double ratio R for light fragments with given mass values are shown with multi-Gaussian function fit.
Concerning the present experiment, the fragment with a certain mass number and kinetic energy were selected for nuclear charge determination via the energy deposition in a ∆Ε-E detector. The spectrum of ∆Ε spectrum dependent on kinetic energies was fitted with multi-Gaussian functions which denote the yield of each charge state. The present nuclear charge resolution is better than that in Ref. [6]. The variation of the widths of the charge distributions with the fragment mass and the kinetic energy, the charge polarization as a function of the fragment mass, the dependence of the mean charge with kinetic energy and mass, as well as proton and neutron odd-even effects are discussed in the following session.

Experimental procedure
A fragment with a given mass number and the ionic charge state q at a given kinetic energy was selected by the LOHENGRIN spectrograph, and the nuclear charge was determined by the residual energy of the fragment passing through an absorber [3], or by the energy deposition in a ∆Ε detector [11]. In contrast with this method, in the present work a detector system consisting of a grid ionization chamber (GIC) on the left side and a gas ∆Ε detector with a supplementary surface-barrier detector on the right side, which provide both ∆Ε and total kinetic energy of the fragment, was used to investigate the nuclear charge distribution of fragments of spontaneous fission of 252 Cf. The diameter of the 252 Cf deposition is 5mm, the fission rate is 3000 fissions/s, and the total number of coincident events recorded is about 3×10 7 . It is indicated that the gas ∆Ε detector is actually a thin grid ionization chamber. The ∆Ε-E telescope utilized in this work is quite similar to that adopted in Ref. [13].   nature of σ zav as a function of fragment mass [14,15] indicates the presence of the odd-even effect. The calculation results with GEF code [16] are also given in fig. 3, for which a mostly flat trend is exhibited with fluctuations due to the known odd-even effect. Two pronounced peaks at A*=82 and 126 are likely caused by shell structure. The difference in the σ z variation with kinetic energy may be comprehended from the fact that for low kinetic product energies the corresponding excitation energies and, hence, the number of evaporated neutrons will be large; for large neutron number ν their variance σ 2 (ν) is also large and, therefore, a given primary mass A* together with its intrinsic charge distribution will be spread over a wider range of product mass A. As a result, the smaller the kinetic energy of the fission products, the more the charge variance measured should rise compared to the variance of the primary fragments [17]. It is interesting to analyze the evolution of fragment charge distributions up to the highest feasible kinetic energies, namely, in cold fission for which fragments have such low excitation energy that no neutrons are emitted.
The fragments are formed in their ground states and with ground-state deformations.
The fragment elongations in fission vary over a large range and the elongation uncertainty resulting from the quantum-mechanical zero-point vibration seems to be in the order of 1-2 fm [6]. For a typical fragment split 109 Tc and 143 Cs in the spontaneous fission of 252 Cf, the deformation energy for Tc is estimated about 6.5 MeV/fm. Fig.4 shows the σ z variation with kinetic energy on A*=101,103,107 and 109 u which probably represent the typical fragment splits holding large elongation uncertainty, consequently large σ z are produced.
During the charge equilibrium at a fixed mass value, the charge equilibrium mode N/Z is commonly described by a harmonic oscillator having a phonon energy ω  characteristic of giant dipole resonance (a few MeV for a nucleus at scission) [18,19]. This oscillator is coupled to the intrinsic degrees of freedom. Under these condition the variance of charge > < 2 z σ dependent on the nuclear temperature T and the inertial parameter of N/Z mode M.  [20,21], where it shows > < 2 z σ has a linear correlation with dc/dt, which account for the increase trend in highest kinetic energy (E L * > 110 MeV) in fig. 4. Brissot and Bocquet [18] have clearly exhibit that the collapse of neck is 5 times faster for 250 Cf* than 230 Th*. The increase of σ z indicates that the velocity of pinching of neck fast increase with the highest kinetic energies for cold fission.

Charge polarization
An important approach regarding the nuclear charge distribution in fission is to investigate the behavior of the average nuclear charge pav Z with respect to its deviation ΔZ from the unchanged charge distribution (UCD), as a function of the mass number of primary fragments A* or the most probable charge [22].
where H and L designate the heavy and light fragments, respectively. Z F and A F are charge and mass of the fissioning system. ν A is the number of neutrons emitted by the corresponding fission fragment. Accordingly ν A for the heavy and light fission product mass is given as [22] ), 143 ( 062 .

Energy dependence of the most probable charge
Kinetic fragment energies dependence of the most probable charge Z p are shown in fig. 6 where the primary mass number of light fragment are given. The obvious increasing tendencies for Z p with the kinetic energies are emerged from the figure which is measured for the first time. It can be seen that Z p of light fragment mass chains vary with energy in similar ways. It is likely that the nuclear charge distribution between the primary fragments is controlled by a process that is unaltered by additional excitation in compound nucleus; hence, the resultant change in Z p with kinetic energy (or excitation energy) is due only to increased neutron emission at higher excitations [25]. This similar variation in Z p with energy adds support to the assumption of an identical charge dispersion in the mass chains. The energy (E L *>110 MeV) is well above average and, in fact, one is approaching cold fission, where all of the available reaction energy Q(A, Z) is converted into fragment kinetic energy. Upon coming close to cold fission, it is found that in most cases the charge number Z(A) maximizing the yield Y(Z|A) for given mass number A coincides with the charge maximizing reaction energy Q(Z|A). The shift of Z p of charge distribution in a given isobaric chain is connected only with prompt neutron emission, which shifts fragment nucleus closer to the valley of β-stability. Secondly, it is related with a decrease of the charge polarization in primary fission fragments, which leads to a decrease of charge density of light fragments and an increase of charge density of heavy fragments [26].
As the excitation energy of the compound nucleus increases the primary heavy fragments therefore are approaching the line of β-stability and primary light fragments are moving off it. This effect reduces the most probable charge of light fission products and raises it for heavy products. formula [27] are also exhibited in the figure. ), ), It can be seen from this figure that the present data are in a perfect agreement with the results calculated with Waldo's formula [27].

Odd-even effect
A correlation between the odd-even effect and fissility is apparent, the proton odd-even effect [10] can be expressed by a function of the Coulomb parameter δ where a = e 17.5 and b = 0.01049. The proton odd-even effect of spontaneous fission nucleus 252 Cf is not conspicuous to compare to that of 230 Th and 233 U [10]. It is worthwhile to investigate the odd-even fluctuations of fragment average charge yield as a function of fragment kinetic (or excitation) energy.
The odd-even staggering of average charge yield in the light fragment group increases with the light fragment kinetic energy E L *, as is shown in fig. 8. At high kinetic energies a large percentage of even atomic numbers is present than at low energies. In the other words, fragments with even charge numbers Z will on average exhibit higher kinetic energies than those with odd Z. The average charge yields of Z L = 46 (or 47) occupying large percentage is palpably visible. One may speculate whether this feature is influenced by the closed Z H = 50 proton shell of heavy fragments. The proton odd-even effect δ p in present measurement and that of Ref. [28] are shown in Table 1. The average yields of light fragment group as a function of neutron number N for different kinetic energies are shown in fig. 9. For the near-barrier fission reaction, the nucleus is expected to be perfectly paired at the saddle point since not enough energy is available at that point to break pairs. Neutron odd-even effect has received less attention because any primary effects are masked by neutron evaporation. The neutron odd-even effect is rather small, the rise is spectacular for large fragment kinetic energy.
At high kinetic energy the fragment excitation energies exhibiting the emission of neutron and gamma will be low. Hence, the energy dependence neutron odd-even effect points to a huge primary neutron effect for very asymmetry fission. Fission with very asymmetric mass splits carries the signature of cold deformed fission in which fragment kinetic energies are high, and odd-even effects are pronounced. To some extent, the limited mass resolution of experimental setup impacts the odd-even effects, especially for the very asymmetric fission which has low yield by several order of magnitude.
In fig. 9 the low kinetic energy corresponding to high excitation energy, the If the mass resolution is improved by using the E-V or 2V method in the fission TOF spectrometer, the odd-even effects will be more clear and visible.

Summary
The measurement for charge distributions of fragments in spontaneous fission 252 Cf has been performed by using a unique style of detector setup consisting of a typical grid ionization chamber and a ∆Ε−Ε particle telescope，in which a thin grid ionization chamber served as the ∆Ε-section and the E-section was a surface barrier detector. The typical physical quantities of fragments, such as mass number and kinetic energies as well as the deposition in the gas ∆Ε detector and E detector were As a result of the study the fragment mass dependency of the average width of the charge distribution shows a systematic decreased trend with the obvious odd-even effect. As for the variation of widths of charge distribution with light fragment products kinetic energies, the approximate V-shape curves have been observed due to the large number of neutron emission for the low kinetic energies (or the high excitation energies), and the approaching cold fission for high kinetic energies (E L *>107 MeV). In the case of the behavior of the average most probable nuclear charge pav Z with respect to its deviation ΔZ from the unchanged charge distribution (UCD) as a function of the mass number of primary fragments A*, for asymmetric fission products (A L *<120) ΔZ is negative value which exhibits marked fluctuations due to odd-even effects, while upon approaching mass symmetry (A L *≥120) ΔZ turns positive and does not fluctuate. It is likely that for asymmetric mass split region the fragments are polarized in charge with more than half a proton being transferred from the heavy to the light fragment. The heavy fragments with the closed proton shell Z=50 may play an essential role, the charge deviation ΔZ reverts sign. Concerning the energy dependence of the most probable charge Z p for given primary mass number A*, the obvious increasing tendencies for Z p with the kinetic energies E L * are observed.
The reason causes this phenomenon is due only to increased neutron emission at higher excitations. The correlation between the average nuclear charge and the primary mass number is given as linear function, which is in a perfect agreement with the calculation results from Waldo's formula. The proton and neutron odd-even effects with light fragment kinetic energies are derived. The odd-even staggering of charge yield in the light fragment group increases with the light fragment kinetic energy.