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Sun Potansiyel ile Etkileşen Vektör Bozonlarının Saçılma Durumu Çözümleri

Yıl 2023, Cilt: 9 Sayı: 2, 333 - 343, 31.12.2023

Ahmet Tas

https://doi.org/10.29132/ijpas.1369826

Öz

Spini-1 olan vektör bozonlar için Sun potansiyeli varlığında Duffin-Kemmer-Petiau denklemi ele alınarak saçılma durumu çözümleri elde edilmiştir. Elde edilen çözümler kullanılarak faz kayması ve saçılma genliği için bağıntılar türetilmiştir. Ayrıca saçılma genliğini sonsuza götürerek bağlı durum enerji özdeğerleri denklemi elde edilmiştir. Mathematica yazılım programı aracılığıyla elde edilen sonuçlar grafiksel ve nümerik olarak verilmiştir. Bunlara ek olarak etkileşme fonksiyonunda yer alan değişkenlerin elde edilen sonuçlara olan etkileri tartışılmıştır.

Anahtar Kelimeler

Saçılma durumları Bağlı Durumlar Duffin-Kemmer-Petiau denklemi Sun Potansiyeli

Kaynakça

  • Bahar, M. K. (2013). AIM solutions to the DKP equation for spin-1 particles in the presence of kratzer potential in (2+1) dimensions. Few-Body Systems, 54, 2133-2142.
  • Bahar, M. K and Yasuk, F. (2013). Relativistic spin-1 particles with position-dependent mass under the Coulomb interaction: Exact analytical solutions of the DKP equation. Canadian Journal of Physics, 91(3), 191-197.
  • Bahar, M. K. and Yasuk, F. (2014). Ansatz approach solution of the Duffin–Kemmer–Petiau equation for spin-1 particles with position-dependent mass in the presence of Kratzer-type potential. Canadian Journal of Physics, 92(12), 1565-1569.
  • Bahar, M. K. and Yasuk, F. (2014). Relativistic solutions for the spin-1 particles in the two-dimensional Smorodinsky–Winternitz potential. Annals of Physics, 344, 105-117.
  • Castro, L.B. and De Castro, A.S. (2014). Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations. Physical Review A., 90(2), 022101.
  • Duffin, R. J. (1938). On the characteristic matrices of covariant systems. Physical Review, 54(12), 1114.
  • Edet, C.O., Amadi, P.O., Okorie, U.S., Taş, A., Ikot, A.N. and Rampho, G. (2020). Solutions of Schrödinger equation and thermal properties of generalized trigonometric Pöschl-Teller potential. Revista mexicana de física, 66(6), 824-839.
  • Flügge, S. (1999). Practical quantum mechanics (Vol. 177). Springer Science & Business Media.
  • Gribov, V. (1999). QCD at large and short distances (annotated version). The European Physical Journal C-Particles and Fields, 10, 71-90.
  • Hamzavi, M. and Ikhdair, S.M. (2013). Approximate solution of the Duffin–Kemmer–Petiau equation for a vector Yukawa potential with arbitrary total angular momenta. Few-Body Systems, 54(11), 1753-1763.
  • Hassanabadi, H., Forouhandeh, S.F., Rahimov, H., Zarrinkamar, S. and Yazarloo, B.H. (2012). Duffin–Kemmer–Petiau equation under a scalar and vector Hulthen potential; an ansatz solution to the corresponding Heun equation. Canadian Journal of Physics, 90(3), 299-304.
  • Hassanabadi, H., Yazarloo, B., Zarrinkamar, S. and Rajabi, A.A. (2011). Duffin-Kemmer-Petiau equation under a scalar Coulomb interaction. Physical Review C, 84(6), 064003.
  • Ikot, A.N., Molaee, Z., Maghsoodi, E., Zarrinkamar, S., Obong, H.P., & Hassanabadi, H. (2015). Analytical solutions of the DKP equation under Tietz-Hua potential in (1+ 3) dimensions. Physics of Particles and Nuclei Letters, 12, 275-281.
  • Jia, C.S., Wang, J.Y., He, S. and Sun, L.T. (2000). Shape invariance and the supersymmetry WKB approximation for a diatomic molecule potential. Journal of Physics A: Mathematical and General, 33(39), 6993.
  • Kemmer, N. (1939). The particle aspect of meson theory. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 173(952), 91-116.
  • Kozack, R.E., Clark, B.C., Hama, S., Mishra, V.K., Mercer, R.L. and Ray, L. (1989). Spin-one Kemmer-Duffin-Petiau equations and intermediate-energy deuteron-nucleus scattering. Physical Review C, 40(5), 2181.
  • Landau, L.D. and Lifshitz, E.M. (1977). Quantum Mechanics, Non-Relativistic Theory. Pergamon, New York.
  • Liang, G.C., Tang, H.M. and Jia, C.S. (2013). Equivalence of the Sun and Tietz potential models for diatomic molecules. Computational and Theoretical Chemistry, 1020, 170-172.
  • Molaee, Z., Ghominejad, M., Hassanabadi, H. and Zarrinkamar, S. (2012). S-wave solutions of spin-one DKP equation for a deformed Hulthén potential in (1+ 3) dimensions. The European Physical Journal Plus, 127(9), 1-8.
  • Nedjadi, Y. and Barrett, R.C. (1993). On the properties of the Duffin-Kemmer-Petiau equation. Journal of Physics G: Nuclear and Particle Physics, 19(1), 87.
  • Nedjadi, Y. and Barrett, R.C. (1994). The Duffin-Kemmer-Petiau oscillator. Journal of Physics A: Mathematical and General, 27(12), 4301.
  • Nedjadi, Y. and Barrett, R.C. (1994). Solution of the central field problem for a Duffin–Kemmer–Petiau vector boson. Journal of Mathematical Physics, 35(9), 4517-4533.
  • Okorie, U.S., Taş, A., Ikot, A.N., Osobonye, G.T. and Rampho, G.J. (2021). Bound states and scattering phase shift of relativistic spinless particles with screened Kratzer potential. Indian Journal of Physics, 1-10.
  • Oluwadare, O.J. and Oyewumi, K.J. (2017). Scattering state solutions of the Duffin-Kemmer-Petiau equation with the Varshni potential model. The European Physical Journal A, 53(2), 1-6, 2017.
  • Oluwadare, O.J. and Oyewumi, K.J. (2018). Approximate scattering state solutions of DKPE and SSE with Hellmann Potential. Advances in High Energy Physics, Vol. 2018.
  • Onate, C.A., Ojonubah, J.O., Adeoti, A., Eweh, J.E. and Ugboja, M. (2014). Approximate eigen solutions of DKP and Klein-Gordon equations with Hellmann potential. African Review of Physics, 9(006), 497-504.
  • Pekeris, C.L. (1934). The rotation-vibration coupling in diatomic molecules. Physical Review, 45(2), 98.
  • Petiau, G. (1936). Contribution a la theorie des equations dondes corpusculaire. Ph.D. Thesis, University of Paris, Published in Acad. Roy. de Belg., Classe Sci., Mem in 8◦ 16(2).
  • Sun, J. X. (1999). Exactly solvable potential with four parameters for diatomic molecules, Acta Physica Sinica, 48, 1992–1998.
  • Taş, A. (2021). Frost-Musulin Potansiyelinin Varlığında (1+ 3) Boyutta Duffin-Kemmer-Petiau Denkleminin l-Dalga Çözümleri. Süleyman Demirel University Journal of Science, 16(2).
  • Taş, A., Aydoğdu, O. and Salti, M. (2017). Dirac particles interacting with the improved Frost–Musulin potential within the effective mass formalism. Annals of Physics, 379, 67-82.
  • Taş, A., Aydoğdu, O. and Saltı, M. (2018). Relativistic spinless particles with position dependent mass: Bound states and scattering phase shifts. Journal of the Korean Physical Society, 70(10), 896-904.
  • Taş, A. and Havare, A. (2017). Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential. Chinese Physics B, 26(10), 100301.
  • Taş A. and Havare, A. (2018). Bound and Scattering States Solution of the Relativistic Spinless Particles in View of the Multiparameter Potential. Few-body systems, 59(4), 1-16.
  • Yanar, H., Taş, A., Saltı, M. and Aydoğdu O. (2020). Ro-vibrational energies of CO molecule via improved generalized Pöschl–Teller potential and Pekeris-type approximation. The European Physical Journal Plus, 135(3), 1-14.
  • Zarrinkamar, S. Panahi, H. and Rezaei, M. (2016). The generalized Coulomb interactions for relativistic scalar bosons. Physics of Particles and Nuclei Letters, 13(4), 436-441, 2016.
  • Zarrinkamar, S., Rajabi, A. A., Yazarloo, B.H. and Hassanabadi, H. (2013). An approximate solution of the DKP equation under the Hulthén vector potential. Chinese Physics C, 37(2), 023101.

Scattering State Solutions of Vector Bosons Interacting with Sun Potential

Yıl 2023, Cilt: 9 Sayı: 2, 333 - 343, 31.12.2023

Ahmet Tas

https://doi.org/10.29132/ijpas.1369826

Öz

For vector bosons with spin-1, scattering state solutions have been attained by considering the Duffin-Kemmer-Petiau equation with the Sun interaction field. Based on the obtained solution, relations for phase shift and scattering amplitude have been derived. Furthermore, the bound state energy eigenvalue relation has been derived by taking the scattering amplitude to infinity. The results obtained through the Mathematica software program are presented graphically and numerically. In addition, the effects of the variables in the interaction function on the obtained results are discussed.

Anahtar Kelimeler

Scattering States Bound States Duffin-Kemmer-Petiau Equation Sun Potential

Kaynakça

  • Bahar, M. K. (2013). AIM solutions to the DKP equation for spin-1 particles in the presence of kratzer potential in (2+1) dimensions. Few-Body Systems, 54, 2133-2142.
  • Bahar, M. K and Yasuk, F. (2013). Relativistic spin-1 particles with position-dependent mass under the Coulomb interaction: Exact analytical solutions of the DKP equation. Canadian Journal of Physics, 91(3), 191-197.
  • Bahar, M. K. and Yasuk, F. (2014). Ansatz approach solution of the Duffin–Kemmer–Petiau equation for spin-1 particles with position-dependent mass in the presence of Kratzer-type potential. Canadian Journal of Physics, 92(12), 1565-1569.
  • Bahar, M. K. and Yasuk, F. (2014). Relativistic solutions for the spin-1 particles in the two-dimensional Smorodinsky–Winternitz potential. Annals of Physics, 344, 105-117.
  • Castro, L.B. and De Castro, A.S. (2014). Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations. Physical Review A., 90(2), 022101.
  • Duffin, R. J. (1938). On the characteristic matrices of covariant systems. Physical Review, 54(12), 1114.
  • Edet, C.O., Amadi, P.O., Okorie, U.S., Taş, A., Ikot, A.N. and Rampho, G. (2020). Solutions of Schrödinger equation and thermal properties of generalized trigonometric Pöschl-Teller potential. Revista mexicana de física, 66(6), 824-839.
  • Flügge, S. (1999). Practical quantum mechanics (Vol. 177). Springer Science & Business Media.
  • Gribov, V. (1999). QCD at large and short distances (annotated version). The European Physical Journal C-Particles and Fields, 10, 71-90.
  • Hamzavi, M. and Ikhdair, S.M. (2013). Approximate solution of the Duffin–Kemmer–Petiau equation for a vector Yukawa potential with arbitrary total angular momenta. Few-Body Systems, 54(11), 1753-1763.
  • Hassanabadi, H., Forouhandeh, S.F., Rahimov, H., Zarrinkamar, S. and Yazarloo, B.H. (2012). Duffin–Kemmer–Petiau equation under a scalar and vector Hulthen potential; an ansatz solution to the corresponding Heun equation. Canadian Journal of Physics, 90(3), 299-304.
  • Hassanabadi, H., Yazarloo, B., Zarrinkamar, S. and Rajabi, A.A. (2011). Duffin-Kemmer-Petiau equation under a scalar Coulomb interaction. Physical Review C, 84(6), 064003.
  • Ikot, A.N., Molaee, Z., Maghsoodi, E., Zarrinkamar, S., Obong, H.P., & Hassanabadi, H. (2015). Analytical solutions of the DKP equation under Tietz-Hua potential in (1+ 3) dimensions. Physics of Particles and Nuclei Letters, 12, 275-281.
  • Jia, C.S., Wang, J.Y., He, S. and Sun, L.T. (2000). Shape invariance and the supersymmetry WKB approximation for a diatomic molecule potential. Journal of Physics A: Mathematical and General, 33(39), 6993.
  • Kemmer, N. (1939). The particle aspect of meson theory. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 173(952), 91-116.
  • Kozack, R.E., Clark, B.C., Hama, S., Mishra, V.K., Mercer, R.L. and Ray, L. (1989). Spin-one Kemmer-Duffin-Petiau equations and intermediate-energy deuteron-nucleus scattering. Physical Review C, 40(5), 2181.
  • Landau, L.D. and Lifshitz, E.M. (1977). Quantum Mechanics, Non-Relativistic Theory. Pergamon, New York.
  • Liang, G.C., Tang, H.M. and Jia, C.S. (2013). Equivalence of the Sun and Tietz potential models for diatomic molecules. Computational and Theoretical Chemistry, 1020, 170-172.
  • Molaee, Z., Ghominejad, M., Hassanabadi, H. and Zarrinkamar, S. (2012). S-wave solutions of spin-one DKP equation for a deformed Hulthén potential in (1+ 3) dimensions. The European Physical Journal Plus, 127(9), 1-8.
  • Nedjadi, Y. and Barrett, R.C. (1993). On the properties of the Duffin-Kemmer-Petiau equation. Journal of Physics G: Nuclear and Particle Physics, 19(1), 87.
  • Nedjadi, Y. and Barrett, R.C. (1994). The Duffin-Kemmer-Petiau oscillator. Journal of Physics A: Mathematical and General, 27(12), 4301.
  • Nedjadi, Y. and Barrett, R.C. (1994). Solution of the central field problem for a Duffin–Kemmer–Petiau vector boson. Journal of Mathematical Physics, 35(9), 4517-4533.
  • Okorie, U.S., Taş, A., Ikot, A.N., Osobonye, G.T. and Rampho, G.J. (2021). Bound states and scattering phase shift of relativistic spinless particles with screened Kratzer potential. Indian Journal of Physics, 1-10.
  • Oluwadare, O.J. and Oyewumi, K.J. (2017). Scattering state solutions of the Duffin-Kemmer-Petiau equation with the Varshni potential model. The European Physical Journal A, 53(2), 1-6, 2017.
  • Oluwadare, O.J. and Oyewumi, K.J. (2018). Approximate scattering state solutions of DKPE and SSE with Hellmann Potential. Advances in High Energy Physics, Vol. 2018.
  • Onate, C.A., Ojonubah, J.O., Adeoti, A., Eweh, J.E. and Ugboja, M. (2014). Approximate eigen solutions of DKP and Klein-Gordon equations with Hellmann potential. African Review of Physics, 9(006), 497-504.
  • Pekeris, C.L. (1934). The rotation-vibration coupling in diatomic molecules. Physical Review, 45(2), 98.
  • Petiau, G. (1936). Contribution a la theorie des equations dondes corpusculaire. Ph.D. Thesis, University of Paris, Published in Acad. Roy. de Belg., Classe Sci., Mem in 8◦ 16(2).
  • Sun, J. X. (1999). Exactly solvable potential with four parameters for diatomic molecules, Acta Physica Sinica, 48, 1992–1998.
  • Taş, A. (2021). Frost-Musulin Potansiyelinin Varlığında (1+ 3) Boyutta Duffin-Kemmer-Petiau Denkleminin l-Dalga Çözümleri. Süleyman Demirel University Journal of Science, 16(2).
  • Taş, A., Aydoğdu, O. and Salti, M. (2017). Dirac particles interacting with the improved Frost–Musulin potential within the effective mass formalism. Annals of Physics, 379, 67-82.
  • Taş, A., Aydoğdu, O. and Saltı, M. (2018). Relativistic spinless particles with position dependent mass: Bound states and scattering phase shifts. Journal of the Korean Physical Society, 70(10), 896-904.
  • Taş, A. and Havare, A. (2017). Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential. Chinese Physics B, 26(10), 100301.
  • Taş A. and Havare, A. (2018). Bound and Scattering States Solution of the Relativistic Spinless Particles in View of the Multiparameter Potential. Few-body systems, 59(4), 1-16.
  • Yanar, H., Taş, A., Saltı, M. and Aydoğdu O. (2020). Ro-vibrational energies of CO molecule via improved generalized Pöschl–Teller potential and Pekeris-type approximation. The European Physical Journal Plus, 135(3), 1-14.
  • Zarrinkamar, S. Panahi, H. and Rezaei, M. (2016). The generalized Coulomb interactions for relativistic scalar bosons. Physics of Particles and Nuclei Letters, 13(4), 436-441, 2016.
  • Zarrinkamar, S., Rajabi, A. A., Yazarloo, B.H. and Hassanabadi, H. (2013). An approximate solution of the DKP equation under the Hulthén vector potential. Chinese Physics C, 37(2), 023101.
Toplam 37 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Atom ve Molekül Fiziği, Kuantum Mekaniğinin Temelleri
Bölüm Makaleler
Yazarlar

Ahmet Tas 0000-0002-1226-5634

Erken Görünüm Tarihi 29 Aralık 2023
Yayımlanma Tarihi 31 Aralık 2023
Gönderilme Tarihi 2 Ekim 2023
Kabul Tarihi 14 Kasım 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 9 Sayı: 2

Kaynak Göster

APA Tas, A. (2023). Scattering State Solutions of Vector Bosons Interacting with Sun Potential. International Journal of Pure and Applied Sciences, 9(2), 333-343. https://doi.org/10.29132/ijpas.1369826
AMA Tas A. Scattering State Solutions of Vector Bosons Interacting with Sun Potential. International Journal of Pure and Applied Sciences. Aralık 2023;9(2):333-343. doi:10.29132/ijpas.1369826
Chicago Tas, Ahmet. “Scattering State Solutions of Vector Bosons Interacting With Sun Potential”. International Journal of Pure and Applied Sciences 9, sy. 2 (Aralık 2023): 333-43. https://doi.org/10.29132/ijpas.1369826.
EndNote Tas A (01 Aralık 2023) Scattering State Solutions of Vector Bosons Interacting with Sun Potential. International Journal of Pure and Applied Sciences 9 2 333–343.
IEEE A. Tas, “Scattering State Solutions of Vector Bosons Interacting with Sun Potential”, International Journal of Pure and Applied Sciences, c. 9, sy. 2, ss. 333–343, 2023, doi: 10.29132/ijpas.1369826.
ISNAD Tas, Ahmet. “Scattering State Solutions of Vector Bosons Interacting With Sun Potential”. International Journal of Pure and Applied Sciences 9/2 (Aralık 2023), 333-343. https://doi.org/10.29132/ijpas.1369826.
JAMA Tas A. Scattering State Solutions of Vector Bosons Interacting with Sun Potential. International Journal of Pure and Applied Sciences. 2023;9:333–343.
MLA Tas, Ahmet. “Scattering State Solutions of Vector Bosons Interacting With Sun Potential”. International Journal of Pure and Applied Sciences, c. 9, sy. 2, 2023, ss. 333-4, doi:10.29132/ijpas.1369826.
Vancouver Tas A. Scattering State Solutions of Vector Bosons Interacting with Sun Potential. International Journal of Pure and Applied Sciences. 2023;9(2):333-4.
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