MINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGY VIETNAM ATOMIC ENERGY INSTITUTE BUI DUY LINH STUDY ON THE SHELL STRUCTURE OF THE NEUTRON RICH ISOTOPES 49Cl AND 49Ar THROUGH ONE N[.]
MINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGY VIETNAM ATOMIC ENERGY INSTITUTE BUI DUY LINH STUDY ON THE SHELL STRUCTURE OF THE NEUTRON-RICH ISOTOPES 49 Cl AND 49 Ar THROUGH ONE-NUCLEON REMOVAL 50 Ar(p,2p) AND 50 Ar(p,pn) REACTIONS Major: Nuclear and Atomic Physics Code: 9.44.01.06 SUMMARY OF DOCTORAL DISSERTATION OF PHYSICS Hanoi - 2022 Contents Introduction 1 MOTIVATIONS 1.1 Shell evolution N = 32 1.2 Experimental Technique 1.3 Theory calculations 3 THE THIRD SEASTAR CAMPAIGN 2.1 Acceleration of a 53 K primary beam 2.2 BigRIPS separator 2.3 SAMURAI setup 5 5 SETUP DATA ANALYSIS 3.1 Particle identification 3.1.1 Particle identification method 3.1.2 Particle identification in BigRIPS 3.1.3 Particle identification in SAMURAI 3.2 Calibration for the secondary reactions 3.2.1 DALI2+ calibration 3.2.2 MINOS calibration 3.3 Doppler correction 3.4 Gamma spectrum analysis 3.4.1 Geant4 simulation 3.4.2 Bremsstrahlung subtraction 3.4.3 Fitting 3.4.4 Test case of (p,2p) and (p,pn) channels 3.5 Cross sections 7 7 7 8 9 10 10 11 11 RESULTS AND DISCUSSION 4.1 50 Ar(p,2p)49 Cl channel 4.1.1 Energy spectrum 4.1.2 Gamma-gamma coincidences 4.1.3 Momentum distribution 4.1.4 Discussion 4.2 50 Ar(p,pn)49 Ar channel 4.2.1 Energy spectrum 4.2.2 Gamma-gamma coincidences 4.2.3 Momentum distribution 4.2.4 Discussion 13 13 13 14 15 16 17 17 18 19 19 Conclusion and outlook 21 References 22 i INTRODUCTION The atomic nucleus is a dominated by system by nuclear forces and quantum mechanics This is evidenced by the shell structure of nucleons In 1949, M Goeppert-Mayer and the research group of O Haxel, J Jensen, H Suess independently published the results of an experiment that observed the energy (energy gap) between two shells Nuclei are with a filled major shell (known as a closed shell) by protons or neutrons are called magic nuclei and have a sphere shape The magic numbers in the nucleus are 2, 8, 20, 28, 50, 82, 126 A magic nucleus is more stable than others, and this means the excitation energy required to transfer the nucleon to the next shell is significantly larger than their nuclear "neighbors." This special feature is used to search for the magic nuclei far from the stability However, recent studies of exotic nuclei far from stability discovered common magic numbers (8, 20, 28, 50, 82, 126) could be altered, while new magic number (14, 32, 34) can appear The evidence for nuclear shell changes (so-called nuclear shell evolution) has been explored at the magic number N = 32, 34 in 52,54 Ca or close shell N = 32 in 50 Ar The properties of the ground state of 50 Ar (Z = 18, N = 32) and a shell structure of 49 Ar (Z = 18, N = 31) is of great interest because they are expected to provide a necessary information on the migration of the pf neutron shell below Ca In parallel with the change of the neutron shell structure, when adding a few neutrons to a chain isotope, the proton orbitals are also changed In K isotopes with N = 20 to 28, experimental results were confirmed for the inversion of the spin-parity J π = 3/2+ for the ground state and J π = 1/2+ for the first excited state, respectively to holes in orbitals 0d3/2 and 1s1/2 A prediction from the shell model of a similar phenomenon occurs in the Cl isotopes 49 Cl (Z = 17, N = 32) is a study candidate for the evolution of both neutron and proton shells in Cl chain In this thesis, the shell structure of the 49 Cl and 49 Ar isotopes will be studied through universal gamma and momentum distribution combined with the theoretical calculation The first γ-ray spectroscopy of 49 Cl and 49 Ar was performed at the Radioactive Isotope Beam Factory with 50 Ar projectiles at 217 MeV/nucleon at the middle of the target The interested nuclei were produced through onenucleon removal reactions of 50 Ar(p,2p) and 50 Ar(p,pn) on the liquid hydrogen target of the MINOS device This device was made with a length of 150 mm to increase the total amount of nuclear reactions Proton tracks in a TPC are used to reconstruct the reaction points Prompt de-excitation γ rays were measured with the NaI(Tl) array DALI2+ , while the momentum distributions were obtained with the SAMURAI spectrometer The TOF-Bρ-∆E method allowed unambiguous identification of the incoming and outgoing nuclei in the BigRIPS and SAMURAI spectrometers, respectively After a new re-calibration and correction parameters were applied for raw data to obtain the best particle identification, the procedure analyses of the gamma spectroscopy and the momentum distribution permitted building the level scheme and calculating cross-sections of 49 Ar and 49 Cl Through the one-proton removal reaction 50 Ar(p,2p), a spin-parity J π = 3/2+ is assigned for the ground state of 49 Cl, similar to the recently studied N = 32 isotope 51 K The first excited state at 350 keV is decided on J π = 1/2+ , while Author: Bui Duy Linh the excited state at 1515 keV is deduced J π = 5/2+ For the one-neutron removal reaction 50 Ar(p,pn), a tentative spin-parity could be determined for the low-lying states of 49 Ar A spin-parity J π = 3/2− is suggested for the ground state hence the first excited state at 198 keV has J π = 1/2− The excited state at 1340 keV is confirmed J π = 7/2− In addition, two excited states at 1050 keV and 1466 keV are proposed J π = 5/2− and J π = 3/2− , respectively Besides, the ground state configuration of the 50 Ar isotope is based on one-nucleon removal reactions, which will be discussed Investigation results of the shell structure evolution in 49 Ar and 49 Cl were compared to state-of-the-art theoretical predictions They include shell-model calculations using SDPF-MU effective interaction or ab initio methods; reaction model calculations using the transfer to continuum method (TC) or distorted-wave impulse-approximation (DWIA) The experimental results in the thesis agreed with the theoretical predictions above, which is the basis for developing more accurate theoretical calculation models My thesis is organized as follows: Chapter presents an introduction, the motivation, thesis objective, the experimental method, and overview theory used in this work Chapter describes in detail the experimental setup and the technical points The calibrations and corrections for raw data are essential to obtain precise analysis results, described in Chapter Besides, this chapter gives a detailed description of the analysis of the γ-ray After validation of the Geant4 for the simulated response functions of DALI2+ , the fit method for the spectra using those response functions will be presented These processes are applied to two reference measurements to benchmark the analysis procedure In Chapter 4, we present the analysis results and compare those with the theory Finally, this study is a conclusion and future outlook CHAPTER 1: MOTIVATIONS 1.1 Shell evolution N = 32 The origin of the new magic number N = 34 far from stability is proposed in [1] as due to the attractive πf7/2 −νf5/2 interaction: when protons are removed on the πf7/2 orbital from 60 Fe to 54 Ca, the νf5/2 orbital is pushed back at higher energy, which decreases the density level In shell model calculations performed with the SDPF-MU interaction [2], the 2+ state for 52 Ca is understood as a neutron excitation νp3/2 → νp1/2 from a ground state dominated by a ν(p43/2 ) configuration (about 90%) Therefore, the large value of the excitation energy is representative of an energy gap at N = 32 With two protons less for 50 Ar, the same calculation predicts mixed configurations + + + for the 0+ , 21 and 41 , so that the E(21 ) value is not so directly connected to an energy gap The one-neutron knockout reaction 50 Ar(p,pn)49 Ar is expected to provide information on hole states in 50 Ar and the sub-shell closure N = 32, two protons away from the doubly closed-shell 52 Ca [3] Of particular interest would be to determine the excitation energy and spectroscopic factor of the low-lying 3/2− , 1/2− and 7/2− states to evaluate the sub-shell closure N = 32 for Ar isotopes in connection with theoretical predictions Increasing collectivity is expected when moving away from the closedshell Ca core With two fewer protons, the Ar isotopes are well suited for the study of collective effects and can be compared to the calcium isotones A similar comparison may be performed on the odd partners, potassium and + chlorine isotopes The 3/2+ ground state and 1/21 first excited state were identified in 37,39 Cl as proton-hole states with large spectroscopic factors exhausting most of the corresponding strength [4, 5] Above N = 22, a possible spin inversion is predicted in theoretical calculations [6], with a very small + 41,43,45 energy difference ∆ = E(1/2+ Cl They were mainly ) − E(3/21 ) for studied with β-decay and in-beam gamma spectroscopy, using various reaction mechanisms like inelastic scattering, deep inelastic scattering, fragmentation, or a few nucleon-removal reactions [6–14] However, no spin parity measurement could be performed, only the absolute value | ∆ | was determined Therefore, the ground state spin parity for 41,43,45 Cl is debatable In Cl isotopes, 49 Cl with N = 32 is interested in the near decades The spin re-inversion is occurred in this isotope Therefore, the one-proton knockout reaction 50 Ar(p,2p)49 Cl is expected to confirm that 1.2 Experimental Technique In this thesis, in-beam γ-ray spectroscopy is used as a tool for studying the isotopes The term in-beam as part of in-beam γ-ray spectroscopy is a reference to a motion Because of the reaction mechanism in the in-flight technique, the γ-ray emissions from residual fragments flight at 0.6 of the speed of light leads to a shift in energy observed in the laboratory frame Therefore, Doppler correction must be performed to obtain energies of the γ-rays in a center-of-mass frame The detector 4π measured the energies and intensities γ-rays emitted during transitions of the nucleus In addition, coincidences between observed transitions are made accessible to the building Author: Bui Duy Linh of detailed level schemes The momentum distribution of residual fragments from knockout reactions is a powerful spectroscopic diagnostic, having widths sensitive to the angular momentum of the removed nucleons and the final states Since the longitudinal and transverse momentum distributions of the recoiled fragments depend on the value of the spectroscopic factor S(nlj) associated with the occupancy of the single-particle orbital nlj [15] Thus, the width of the transverse momentum distribution reflects the size of the target essentially In contrast, the longitudinal momentum distributions can only sample the external part of the nucleon wave function To put it simply, the shape of the momentum distribution reflected the momentum content in the part of the wave function when we accessed the magnitude of the reaction cross-section is determined by this part Besides, a great advantage of inverse kinematics is recoil momentum and energy can be directly measured Combining this with the information from γ-ray spectroscopy, one can use momentum distribution to determine angular momentum ℓ 1.3 Theory calculations The shell model is the basic framework for nuclear structure calculations in terms of nucleons The nuclear shell-model calculation is one of the configuration interaction methods to study nuclear structure in nuclear physics There are two shell-model calculations using in this thesis The first calculation is a shell-model calculation using the KSHELL code detail in [16, 17], which was performed by N Shimizu and Y Utsuno These framework calculations were performed in the SDPF-MU effective interaction [18] and considering the full sd and pf model space for protons and neutrons The second calculation is Ab initio methods, which were calculated by V Soma and D Holt These methods are now able to compute open shell, intermediatemass, odd-even nuclei, either in their full-space [19, 20] or valence-space [21] implementation In my thesis, the momentum analysis can obtain both the parallel momentum distributions (PMDs) and transverse momentum distributions (TMDs) The experimental results will be compared to distributions obtained from various reaction models such as TC method [22] and DWIA method [23, 24] TC calculations are executed M.Gómez-Ramos and A.Moro, while DWIA calculations were performed by N.T.T.Phuc and K.Ogata The results of shell structure analysis of isotopes 49 Cl and 49 Ar will be compared with the most modern theoretical calculation There is a shellmodel calculation using SDPF-MU interaction performed using the KSHELL code A good agreement is obtained for neutron-rich Ca, K, and Ar isotopes with high accuracy and have been confirmed by experimental results [1–3, 18, 25] Besides, the calculation method ab initio has been widely applied in recent years, especially for medium-mass nuclei [25–31] The calculation results using this method also accurately predict the ground state, the excited states in the nuclear region of interest to the thesis [32, 33] CHAPTER 2: THE THIRD SEASTAR CAMPAIGN SETUP 2.1 Acceleration of a 53 K primary beam In the SEASTAR3 campaign, a 70 Zn primary beam was accelerated by the RIBF accelerating system [34] up to an energy of 345 MeV/nucleon and impinged on a 10-mm-thick rotating beryllium production target at the entrance of the BigRIPS separator to produce a cocktail of secondary beams which include 50 Ar The intensity of the 70 Zn was 240 pnA, which corresponds to 1.5 × 1012 particles per second (pps) 2.2 BigRIPS separator The BigRIPS placed after the accelerating system is a large acceptance and a two-stage radioactive ion beam separator The first stage is located between the F0 - F2 focal planes, while the second stage is between F3 - F7 focal planes The first stage of BigRIPS performs to generate and separate secondary beams using the Bρ−∆E −Bρ technique on an event-by-event [35] This method is the time of flight, magnetic rigidity, and energy loss of the isotopes are measured to deduce their mass-to-charge ratio A/Q and their atomic number Z The position-sensitive Parallel Plate Avalanche Counter (PPAC) detector [36] at F3, F5, and F7 used to measure the ion trajectories through the BigRIPS separator, which allows calculating Bρ Two fast timing plastic scintillator detectors [37, 38] were placed at F3 and F7 focal planes (a distance of flight 46.6 m) to obtain the time of flight (TOF) of the particle in BigRIPS The multi-sampling ionization chamber (MUSIC) [39] is used to measure the energy loss (∆E) of the beam ions and installed at F7 2.3 SAMURAI setup After separation and identification at BigRIPS, the isotopes of interest are transferred to SAMURAI area by SAMURAI beam-line branch In this sector, experiment equipment divide three parts: (1) - a time trigger and tracking detectors; (2) - the secondary target and γ-ray detectors; (3) - PID detector at SAMURAI Figure 2.1 presents SAMURAI setup In this figure, plastic scintillators (SBTs) use to time trigger for all measurement in SAMURAI, while The beam trajectory can be extracted from the position information given by two Beam Drift Chambers (BDC1 and BDC2) [40] The secondary target is MINOS (MagIc Numbers Off Stability) device [41, 42] to perform one nucleon knockout reaction This device is a liquid-hydrogen (LH2 ) target and surrounded by Time Projection Chamber (TPC) [43, 44] MINOS is a device dedicated to nucleon removal from very exotic nuclei by the protons in the LH2 target TPC allows to reconstruct the reaction vertex position inside the target length up to 150 mm After one nucleon removal reaction in the liquid-hydrogen target, residue 49 Ar or 49 Cl are immediately emitted prompt gamma-ray These gamma-rays are measured by the DALI2+ array [45–47] The angular coverage of the full DALI2+ array is from 15◦ to 118◦ with respect to the center of the LH2 target [3] An average energy threshold of NaI(Tl) crystals were set to around 50 keV in order to reduce background events For a velocity βin = 0.6 at the entrance of the MINOS target, the photo-peak efficiency and energy Author: Bui Duy Linh resolution at 500 keV (1 MeV) with 15 cm radius add-back are 48% (34%) and 8.2% (8%), respectively 49 Ar or 49 Cl isotopes in the very forward direction are coming to the superconducting dipole magnet (the SAMURAI magnet) This magnet was used to separate charged particles and neutrons in this product using an analysis of the rigidity of the heavy fragments Neutron is measured by NEBULA NeuLAND [48–50] The position of the heavy fragments was measured by two tracking detectors (FDC1 and FDC2) which were placed before and after the SAMURAI magnet The position information from the FDC and the reconstructed rigidity from the superconducting dipole magnet allow us to determine the momentum vector of the heavy fragments A plastic scintillator hodoscope (HODF24) [40] was placed after FDC2 to measure the timing and the energy loss of the heavy fragment for particle identification Figure 2.1: A schematic view of the SAMURAI setup for the third SEASTAR campaign Two red arrows, the gray arrow show the trajectories of a 50 Ar beam particle, a heavy fragment 49 Ar or 49 Cl, and neutrons (a knocked-out and a decay neutrons), respectively See the text for details Image modified from [51] CHAPTER 3: DATA ANALYSIS 3.1 Particle identification 3.1.1 Particle identification method The particle identification (PID) in the BigRIPS and SAMURAI spectrometers is the first step of the data analysis The TOF-Bρ-∆E method is used to identify the incoming and outgoing particles before and after the secondary target, which is done event by event with the determination of their charge Z and of their charge-to-mass ratio A/Q from the measurement of Bρ, ∆E, and Time-Of-Flight (TOF) [35] The details of the TOF-Bρ-∆E identification method are described in our article at Nuclear Science and Technology, Vol.7, No 2, pp 01-07 (2017) [52] 3.1.2 Particle identification in BigRIPS To improve PID quality in BigRIPS, calibrations and corrections need to be performed to remove the noise signals that reduce the resolution in the plastic scintillator, PPAC, and MUSIC detectors Fig 3.1 shows the comparison results of PID with and without corrections Figure 3.1: Particle identification of atomic number (Z) vs mass-to-charge ratio (A/Q) with full statistics of the experiment in BigRIPS: before (a) and after (b) background reduction 50 Ar secondary beams were marked in the red ellipse After applying all the corrections and gates for BigRIPS, the final PID plot of atomic number Z versus mass-over-charge-ratio A/Q identification is presented in figure 3.1-b) Besides, figure 3.1-a) shows PID before background removal, which extracted from online analysis We find an A/Q and Z sigma resolution of 0.070(1) % and 0.973(1) %, respectively For the average of all isotopes, A/Q and Z resolution in sigma are 0.049 % and 0.84 % It is good enough to separate interesting isotopes from other isotopes 3.1.3 Particle identification in SAMURAI To apply a similar method of BigRIPS PID to SAMURAI, such as recalibrations and corrections performed to SBT, BDC, FDC, and HODOF24 detectors After using all the calibrations for the SAMURAI detector, the final PID plot of atomic number Z versus mass-over-charge-ratio A/Q identification for all data in SEASTAR3 is presented in figure 3.2 49 Ar and 49 Cl isotopes were marked in this figure 3.2 Calibration for the secondary reactions After PID of incoming and product beams, re-calibrations and corrections of MINOS and DALI2+ are required to obtain accurate gamma energy emitted Author: Bui Duy Linh 21 20 10 19 Z 10 18 49 Ar 49 Cl 17 16 2.6 2.7 2.8 2.9 10 A/Q Sat Aug 22 11:42:18 2020 Figure 3.2: SAMURAI particle identification diagrams with all data in the SEASTAR3 experiment 49 Ar and 49 Cl were marked in the black ellipse from product isotopes 3.2.1 DALI2+ calibration The energy and time information of DALI2+ will be used; therefore, we need to calibrate both of them Before, during, and after acquiring data in the SEASTAR campaign, there are four standard sources (60 Co, 88 Y, 133 Ba, and 137 Cs) used to calibrate DALI2+ array The calibration procedures were applied independently for each crystal Due to Compton scattering, which one occurs when one γ-rays interact and distribute energy over several NaI crystals That effect changed the signal over the background ratio of the DALI2+ array In order to correct for the energy of these γ-rays, the routine of the add-back is used in the analysis During the add-back procedure, the energies will be summed to reconstruct the initial energy, if the energy deposits of one event within a certain time window and within a certain spherical distance from the crystal with the highest energy detected We are assumed that the crystal receiving the largest part of the reconstructed energy is the one where the first interaction This crystal was determined by Doppler corrections The analysis used a maximum spherical distance of 15 cm 3.2.2 MINOS calibration TPC surrounded the liquid hydrogen target of the MINOS device, which is used to reconstruct each reaction position inside the target and, therefore, to improve the Doppler-correction The MINOS calibration is performed by finding the time t0 , the drift velocity (ϑdrif t ), and the target length (zvertex ) The drift velocity of the electrons in the TPC is needed to set the metric for the proton track lengths Therefore, the drift velocity (vdrif t ) is vital to ensure a proper reconstruction of the position along beam axis z It depends on the pressure and impurities of the gas in a run-by-run, which is not constant Because of that, it is necessary to determine run by run The drift velocity is calculated as follow: vdrif t = LT P C Tstop − Tstart (3.1) where LT P C = 300 mm is the length of the TPC, Tstart and Tstop correspond start time and stop time of each event Two values are determined on the distribution of drift times during each run [44] Author: Bui Duy Linh of the response function for observed peaks corresponding to the intensity (Ai ) Due to low statistics, the principle of maximum likelihood [60] for the fit was used to take into account empty bins and fit the better histogram [58] Besides, the likelihood ratio test was also applied to calculate the significance level for a quantitative criterion of each observed peak [3, 61] Therefore, the criterion identification for each candidate peak is a real peak in the following way: The value of χ2 analysis obtain the goodness to fit; The width of the candidate peak must agree with the resolution of the response function at this energy; The significance level of the peak obtained from the likelihood ratio test for the fit is greater than σ 3.4.4 Test case of (p,2p) and (p,pn) channels In order to test the analysis procedures, the reaction of 51 K(p,2p) [62] and Ca(p,pn) [30] channels were used as a benchmark Two channels used the same condition and were set up with my channel in the SEASTAR3 experiment Results are in good agreement with previous studies Evidence validates the analysis method of (p,2p) and (p,pn) reactions Therefore, the cross-check result confirms the validity of the procedure of all steps of our analysis 54 Gamma-gamma coincidences This section only mentions a brief of the γ − γ coincidence method for the transitions The application detail way will present in 49 Cl and 49Ar in chapter The method has ways: (1) γ − γ coincidences without background subtraction; (2) γ − γ coincidences with background subtraction The γ − γ coincidences without background subtraction were investigated using the 2D matrix The DALI2+ response functions can fit the corresponding spectrum to extract the evidence of the coincident transitions’ energy However, these γ − γ spectra may not be all true coincidences as no background subtraction was performed so far To reduce the number of fake coincidences, background subtraction was performed This background’s false coincidences are estimated and subtracted by setting gates on the high-energy regions, free of other transitions 3.5 Cross sections For each channel, either inclusive cross-section or exclusive crosssections in coincidence with identified transitions are calculated In this section, only the method of cross-section calculation is described The detailed calculation of each channel is shown in the next chapter Inclusive cross-sections were calculated from the number Nin of projectiles entering the target and the number of ejectiles NSAM identified in the 11 Author: Bui Duy Linh focal plane of the SAMURAI spectrometer as σ inc (mb) = NSAM Nin × NT × T (3.7) with an overall transmission T = 0.491(4) including the efficiencies of the beam detectors for 50 Ar case, the absorption of flux in the thick target and the acceptance of the beam line obtained in an empty target measurement The target density NT (at/cm2 ) is given by NT = ρ × L × 6.02 × 1023 1.008 (3.8) with the volumetric mass of liquid hydrogen ρ = 70.973 g/cm3 at atmospheric vapor pressure and the length (L) of the target 15.15 (10) cm, the Avogadro number is 6.02 × 1023 atoms/mol, and MH = 1.008 g/mol Variations of the target density were controlled by an overall measurement of the vapor pressure Charge state changes are not considered in this calculation, in agreement with their detection absence in the ionization chambers and LISE++ calculations predicting 1% or less of charge states in the region When statistics were high enough to carry out exclusive cross-section determination, we obtained for each identified transition i → f a number Nγ of photons as the ratio αi × Nisim γ Ni→f = (3.9) Nin where the normalizing factor αi is obtained from the fit with the response functions for all multiplicities The exclusive cross section σiex (mb) for the state i is obtained as σiex = X f corr Ni→f Nin × NT × εM IN OS × T (3.10) where εM IN OS is the efficiency to detect at least one proton in the TPC corr obtained in a simulation with a 15 cm length target An effective Ni→f is γ used, correcting Ni→f for the feeding from higher-lying states Since the feeding from non-identified transitions cannot be accounted for, the obtained values are higher limits of exclusive cross-sections for one proton removal to the given state 12 CHAPTER 4: RESULTS AND DISCUSSION 50 This chapter is dedicated to the experimental results of 50 Ar(p,2p) and Ar(p,pn) channels 50 4.1 Ar(p,2p)49 Cl channel In the shell-model framework, ten protons in 50 Ar occupy the sd shell valence space with three active orbitals, π0d5/2 , π1s1/2 , and π0d3/2 Then, we can expect from one-proton removal to populate positive parity states in −1 49 Cl, which have a sizable overlap with proton hole configurations π1s1/2 −1 and π0d3/2 in 50 Ar 4.1.1 Energy spectrum In-beam gamma-ray spectroscopy of 49 Cl isotope is studied via the one proton removal 50 Ar(p,2p) reaction after add-back and Doppler correction Due to the low statistics, the multiplicity is unlimited γ rays per event Only one clear transition is found around 350 keV, while there are three structures in the ranges 600 keV to 700 keV, 900 keV to 1000 keV, 1500 keV to 1700 keV Above 2000 keV, no transition is seen The procedure that we established and validated in the chapter was applied to the 49 Cl data The energy of the four peak candidates in the γ-energy spectrum for 50 Ar(p,2p) were identified and determined by χ2 analysis as discussed in section 3.4 The range of the energy of peaks were selected as following: 330 to 376 keV with keV interval 600 to 680 keV with keV interval 880 to 990 keV with keV interval 1400 to 1630 keV with keV interval 0 P r o b a b ility G a u s s ia n F it 3 3 L ife tim e ( p s ) P r o b a b ility ( a u ) 0 0 0 3 4 6 7 9 0 0 E n e rg y (k e V ) 5 5 6 E n e rg y (K e V ) Figure 4.1: The probability density function for the first peak (350 keV) in the (p,2p)49 Cl reaction with all γ multiplicities (Left) The probabilities as a function of the energy (black points) are fitted with a normal distribution (red continuous lines) (Right)The probabilities as a function of the energy and lifetime effect were drawn in the contour graph, and the color indicates the χ2 values The details see in the text We assumed the standardized he probability density function (PDF) approximately obey a normal distribution The PDF example for the first peak, which was used χ2 analysis, is drawn in the figure 4.1 This figure’s 13 Author: Bui Duy Linh 200 Counts Counts / 30 / 30 keV keV 200 150 150 100 100 50 50 1000 (b) 102 Counts / 30 keV Exp data sim + background simulation background (a) 2000 3000 E (keV) 10 1000 2000 3000 E (keV) 49 Figure 4.2: Doppler-corrected γ -ray spectrum of Cl populated from (p,2p) reaction: the experimental data points, the simulated response of each transition (red continuous lines), a two-exponential background (red dashed line), and the sum of these simulated transitions with the background (black line) (a) and (b) present arithmetic and logarithmic scales of the vertical axis, respectively All γ multiplicities are shown left presents the probabilities as a function of the energy, which is the normal distribution with the centroid of 351 keV The one-sigma range corresponds to the statistical error of the peak energy The lifetime effects were investigated The measured photopeaks’ width and shape are sensitive to lifetimes above few tens of picoseconds and were included in the energy uncertainties as mentioned in [55] The figure’s right is the contour graph of the probabilities as a function of the energy and lifetime effect The χ2 value ranges indicated by color from orange to blue correlated with increase value The best χ2 located at the orange region around 350 keV and lifetime