VNU. JOURNAL OF SCIENCE, Mathematics - Physics. T.XXI, N 0 1 - 2005 DETERMINING THE ISOMERIC RATIO OF NUCLEAR REACTION 46 T i (γ,pn) 44 Sc BY EXPERIMENT Tran Tri Vien, Doan Quang Tuyen, Nguyen Trung Tinh College of Science, VNU Abstract. The bremsstrahlung beam with energy end point of 65MeV createdwhenthe e − beam with energy of 65MeV irradiated to thin wolfram target was used to irradiate to TiO 2 sample in order to make the 46 T i (γ, pn) 44m,g Sc reaction. The gamma spectrum of Sc 44m,g was analyzed by the gammavision spectrometry with HPGe detector at linear accelerator laboratory in POSTECH, Korea. As the result, the isomeric ratio Υ m /Υ g of the reaction is presented. 1. Introduction The isomeric ratio data of nuclear take an important role in nuclear structure re- search and nuclear reaction mec h anism, that why, there are many laboratories in the world studying these. In our experiment , the beam of bremsstrahlung radiations is cre- ated when e − current with energy of 65MeV irradiating to thin wolfram - target, then the bremsstrahlung beam irradiating to TiO 2 sample of 99.99% pure degree. After 2 hours of irradiation, the sample disintegrates in a period of time depending on the sample ra- dioactivity. The sample is measured by the geometric arrangement fixed for minimizing the error. The 44 Sc is created by reaction as follows γ + 46 Ti → 44 Sc + n + p. After being produced, 44 Sc nuclei is in excited states. However, the life-time of these states is very short(< 10 −10 sec). Then the nuclei jump into the lower energy states, and at the end, they jump to the isomeric state or ground state. On the other hand, 44 Sc is a radioactive nuclear. It disintegrates to 44 Ca from isomeric state and ground state. The gamma spectrum of 44 Sc created from two parts, one is due to 44 Sc transferred from isomeric state in to ground state, and the other is due to 44 Ca transferred from higher energy excited states to the lower one or to the ground state (Fig.1). 2. Calculating the essential parameters of reaction In this paper the following symbols are used: t 1 is time for irradiating to TiO 2 target, t 2 is the disintegrating time (the period of time from radiation stop to spectral measurement) and t 3 is time spectral measurement. The equation representing the irradiating at sample is as follows dN m dt =N 0 σ m φ(t) − λ m N m (2.1) Typeset by A M S-T E X 51 52 Tran Tri Vien, Doan Quang Tuyen, Nguyen Trung Tinh dN g dt =N 0 σ g φ(t) + P m,g N g − λ g N g , (2.2) where σ m and σ g are cross-sections of the metastable and the ground state, respectively, λ m and λ g are the decay constants of these states, P m,g is the branching ratio for the decay of metastable to ground state, N 0 is the number of target nuclei, φ(t)istheflux of beam per 1cm 2 of bremsstrahlung irradiated in to the sample, N m and N g are the number of nuclei in the metastable and the ground state. Figure 1. Production and deca y of the metastable and the ground state In gamma spectra, the area (number of count) of peak with energy E γ is determined as follows: S=f γ  t 3 8 0 A(t)dtC f γ : intensity of photopeak :detectionefficiency of gamma spectrometry For gamma spectrum of 44 Sc m , the spectral peak area with energy E γ calculated as follows: S m =N m =f m γ  m t 2 +t 3 8 t 2 λ m N m dtC m =f m γ  m N 0 φ 0 σ m λ m (1 − e −λ m t 1 )e −λ m t 2 (1 − e −λ m t 3 )C m (2.3) Determining the isomeric ratio of nuclear reaction 53 Similarly, the area of spectral peaks caused by the disintegration of nuclei 44,g Sc is S g =N g =f g γ  g N 0 φ 0 ^ P m,g σ m λ g λ m (λ g − λm) (1 − e −λ m t 1 )e −λ m t 2 (1 − e −λ m t 3 )  C g +f g γ  g N 0 φ 0 ^ 1 λ g w σ g − P m,g σ m λ g λ g − λm W (1 − e −λ g t 1 )e −λ g t 2 (1 − e −λ g t 3 )  C g , (2.4) where f m γ and f g γ is intensity of gamma ray corresponding with the state of 44,m Sc and 44,g Sc,  γ is detection efficiency of gamma spectrometry at spectral peak with energy E γ ,C m and C g are the self-absorption correction c oefficient of radiated sources, C m a 1, C g a 1. With the result of equations (2.3), (2.4) the isomeric ratio can be determined IR = σ m σ g = ^ λ g (1 − e −λ m t 1 )e −λ m t 2 (1 − e −λ m t c ) λ m (1 − e −λ g t 1 )e −λ g t 2 (1 − e −λ g t c ) w C m N m f m γ  m C g N g f g γ  g − P m,g λ g λ g -λ m W + P m,g λ m λ g − λ m  −1 (2.5) And the error ∆IR IR =  w ∆N m N m W 2 + w ∆N g N g W 2 + w ∆ m  m W 2 + w ∆ g  g W 2 , (2.6) in which C m C g istherateofcorrectioncoefficients and has value of around 1. 3. Experiment 3.1. Experime ntal arrangement The experimental flowchart is arranged as fig.2. Figure 2. Experimental arrangement. Gamma spectrum of 44 Sc from Ti(γ, pn)Sc reaction is measured by HPGe gamma spectrometry. The measurement scheme is presented in fig.3, and the gamma spectrum of 44 Sc presented in Fig.4. 54 Tran Tri Vien, Doan Quang Tuyen, Nguyen Trung Tinh . Figure 3. Scheme of analytical system for gamma spectrum of reaction preduction Figure 3. Gamma spectrum of 44 Sc measured by Gammavision Spectrometry 3.2. Calculation of typical peak area In the gamma spectrum of 44 Sc, there are two spectral peaks with energies of 271keV created due to 44 Sc transferring from metastable to ground state and of 1157keV created when the 44 Sc nuclei in both metastable and ground state disintegrate to 44 Ca. With 44m Sc, relative intensity of gamma ray with energy E γ = 271keV and with energy E γ = 1157keV is 86.7:1.31. So that, the count of peak with 271keV energy of metastable state is equal the area of spectral peak of 271keV energy. But, the count number of 1157keV energy peak of ground state is not equal the area of 1157 keV energy peak. It is determined as follows N m =S 271 (3.1) N g =S 1157 − 1.31 g 86.7 m N m , (3.2) where S 271 is the area of 271 keV energy peak and S 1157 is the area of 1157 keV one. Determining the isomeric ratio of nuclear reaction 55 3.3. Isomeric ratio The detection-efficiency of gamma spectrometry with energy of 271 keV and of 1157 keV has been determined in the paper ” Surveying the HPGe gamma detector abso- lute efficiency”, and their value is as follows: at 271 keV energy  m =0.01068 ± 0.00029; at 1157 keV energy:  g =0.00291 ± 0.00007 According to the part mentioned above, we can determine the values of N m and N g . Substituting the parameters int o formula (2.5),wecalculatetheisomericratioof 46 Ti(γ, n) 44 Sc reaction: IR = 0, 112 The error of isomeric ratio calculated according to the formula(2.6) and it’s value is: IR = 0.011 So, the isomeric ratio of reaction 46 Ti(γ, pn) 44m,g Sc is: IR = 0, 112 ± 0.011 4. Conclusion Using the beam of bremsstrahlung with energy end point of 65MeV from the ac- celerator in POSTECH - South Korea, we ha ve determined the isomeric ratio (IR) of the reaction 46 Ti(γ, pn) 44m,g Sc as follows: IR = 0.112 ± 0.011 In order to compare this data with the others, we have consulted a lot of published data and those from in the Internet. But, we could not get any data that is similar to this reaction. Consequently, the result of our experiment can be considered as the new result that may contribute to d atabase of isomeric ratio of nuclear reaction. Acknowledgements: This work is supported by the Science Researc h Program provided by Vietnam National Universit y, Hanoi QG-04-02. References 1. M. Boston, M. N. Erduran, M. Sirin and M. Subast, Isomeric cross-section ratio for the (n,2n) r eaction on 45 Sc from 13.6to24.9MeV, Physical Review,NewYork,V. 56, No 2(1997), pp 918 − 921. 56 Tran Tri Vien, Doan Quang Tuyen, Nguyen Trung Tinh 2. J. R. Huizenga and R. Vandenbosch, Interpretation of isomeric cross-section ratio for (n, γ)and(γ, n) reaction, Physical Review, New York, V.120,(1960), pp 1305−1313. 3. D. Kolev, Studies of some isomeric yield ratios produced with Bremsstrahlung, Appl. Radiati. Isot, Great Britain, V.49, No. 8(1998), pp.989 − 995. 4. D. Kolev, E. Dobreva , N. Nenov and V. Todorov, Aconvenient method for ex- perimental determination of yields and isomeric ratios in photonuclear reaction measured b y the activation technique, Nuclear instruments and methods,North- Holland, A 356(1995), pp 390-396. 5. R. Vanska and R. Rieppo, The experimen tal isomeric cross-section ratio in nuclear activation ternique, Nuclear instruments and methods, North-Holland, V.179(1981), pp 525-532. 6. Tran Tri Vien, Doan Quang Tuyen, Nguyen Trung Tinh, Surveying the HPGe gamma detector absolute efficiency,VNU, Journal of Science,No2(2004),pp 44-49. . VNU. JOURNAL OF SCIENCE, Mathematics - Physics. T.XXI, N 0 1 - 2005 DETERMINING THE ISOMERIC RATIO OF NUCLEAR REACTION 46 T i (γ,pn) 44 Sc BY EXPERIMENT Tran. As the result, the isomeric ratio Υ m /Υ g of the reaction is presented. 1. Introduction The isomeric ratio data of nuclear take an important role in nuclear