Comparison of the $^{12}\mathrm{C}$$(e,{e}^{\ensuremath{'}}p)$ cross section at low momentum transfer with a relativistic calculation

Comparison of the ${}^{12}C$ $(e, e^{'} p)$ cross section at low momentum transfer with a relativistic calculation

T. Tamae, Y. Sato, T. Yokokawa, Y. Asano, M. Kawabata, O. Konno, I. Nakagawa, I. Nishikawa, K. Hirota, H. Yamazaki, R. Kimura, H. Miyase, H. Tsubota, C. Giusti, and A. Meucci

Phys. Rev. C 80, 064601 – Published 1 December 2009

Abstract

The ( $e, e^{'} p_{0}$ ) cross section of ${}^{12}C$ has been measured at an energy transfer of 60 MeV and a momentum transfer of $104.4$ MeV/ $c$ using a $197.5$ MeV continuous electron beam. The cross section at missing momenta between $181.5$ and $304.8$ MeV/ $c$ obtained from the experiment is compared with theoretical calculations based on the relativistic distorted-wave impulse approximation with and without meson-exchange currents (MEC). The contribution of MEC due to the seagull current is large in the high-missing-momentum region, in particular for the longitudinal component. The cross sections calculated using three different current-conserving operators (cc1, cc2, and cc3) are similar, in contrast to the $(γ, p)$ reaction, where the operators give very different results. The shape of the measured cross section is well described by the calculations, whereas its magnitude is slightly smaller than that described by the calculations.

Received 17 September 2009

DOI:https://doi.org/10.1103/PhysRevC.80.064601

Authors & Affiliations

T. Tamae^*, Y. Sato, T. Yokokawa^†, Y. Asano, M. Kawabata, O. Konno^‡, I. Nakagawa^§, I. Nishikawa, K. Hirota^∥, and H. Yamazaki

Laboratory of Nuclear Science, Graduate School of Science, Tohoku University, Mikamine, Taihaku-ku, Sendai 982-0826, Japan

R. Kimura, H. Miyase, and H. Tsubota

Department of Physics, Graduate School of Science, Tohoku University, Aramaki, Aoba, Sendai 980-8578, Japan

C. Giusti and A. Meucci

Dipartimento di Fisica Nucleare e Teorica, Università di Pavia and Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, I-27100 Pavia, Italy

^*tamae@lns.tohoku.ac.jp
^†Present address: Iwanami Shoten Publishers, 2-5-5, Hitotsubashi, Chiyoda-ku, Tokyo 101-8002, Japan.
^‡Present address: Department of Electrical Engineering, Ichinoseki National College of Technology, Hagiso, Ichinoseki 021-8511, Japan.
^§Present address: RIKEN Nishina Center, Wako, Saitama 351-0198, Japan.
^∥Present address: RIKEN Radiation Lab., Wako, Saitama 351-0198, Japan.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 80, Iss. 6 — December 2009

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
An example of the missing energy spectrum, which was measured at the momentum transfer direction. Events between 13 and 19 MeV were separated into ( $e, e^{'} p_{0}$ ) and ( $e, e^{'} p_{1}$ ) components by fitting the data with two Gaussians using a maximum-likelihood method. The dashed and dotted curves represent the ( $e, e^{'} p_{0}$ ) and ( $e, e^{'} p_{1}$ ) components, respectively, and the solid curve gives their sum.Reuse & Permissions
Figure 2
Cross section of the ${}^{12}C$ $(e, e^{'} p_{0})$ reaction as a function of the angle $ϑ_{p}$ between the outgoing proton and the momentum transfer.Reuse & Permissions
Figure 3
Reduced cross section of ${}^{12}C$ ( $e, e^{'} p_{0}$ ) and ( $γ, p_{0}$ ) reactions as a function of the missing momentum. Closed circles show the results of the present ( $e, e^{'} p_{0}$ ) experiment at $| q | = 104.4$ MeV/ $c$ . Open triangles and open circles represent the results of the ${}^{12}C$ ( $e, e^{'} p_{0}$ ) [32] at higher momentum transfers, ranging from 155 to 519 MeV/ $c$ , and ( $γ, p_{0}$ ) [16] reactions, respectively. Curves show the RDWIA calculations corresponding to them. Solid (black), dashed (red), and dotted (green) curves are calculations for cc1, cc2, and cc3 current operators, respectively.Reuse & Permissions
Figure 4
The ${}^{12}C$ $(e, e^{'} p_{0})$ cross section of the present experiment as a function of the missing momentum. Solid, dashed, and dotted lines are the RDWIA results using the cc1, cc2, and cc3 one-body current operators, respectively. The corresponding spectroscopic factors have been applied to the calculations.Reuse & Permissions
Figure 5
The ${}^{12}C$ $(e, e^{'} p_{0})$ cross section of the present experiment as a function of the missing momentum, in comparison with the relativistic calculations involving the one-body $+$ seagull current. Solid, dashed, and dotted lines are obtained using the cc1, cc2, and cc3 one-body current operators, respectively. The dot-dashed line is calculated using the one-body cc2 current without the seagull term. Corrections described in the text have been applied to all the theoretical calculations. A further factor of 0.75 is applied to normalize them to the present experimental value at the lowest missing momentum.Reuse & Permissions
Figure 6
Separated response functions calculated in RDWIA for the cc2 current operator. Thick (black) lines represent the results obtained including the seagull contribution, and thin (red) lines show those without it. Solid, dashed, and dash-dotted lines show the longitudinal, transverse, and transverse-transverse components of the response function, respectively. The spectroscopic factor is not applied in the calculation.Reuse & Permissions

Physical Review C

covering nuclear physics

Comparison of the ${}^{12}C$ $(e, e^{'} p)$ cross section at low momentum transfer with a relativistic calculation

T. Tamae, Y. Sato, T. Yokokawa, Y. Asano, M. Kawabata, O. Konno, I. Nakagawa, I. Nishikawa, K. Hirota, H. Yamazaki, R. Kimura, H. Miyase, H. Tsubota, C. Giusti, and A. Meucci

Phys. Rev. C 80, 064601 – Published 1 December 2009

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review C

covering nuclear physics

Comparison of the C12(e,e′p) cross section at low momentum transfer with a relativistic calculation

T. Tamae, Y. Sato, T. Yokokawa, Y. Asano, M. Kawabata, O. Konno, I. Nakagawa, I. Nishikawa, K. Hirota, H. Yamazaki, R. Kimura, H. Miyase, H. Tsubota, C. Giusti, and A. Meucci

Phys. Rev. C 80, 064601 – Published 1 December 2009

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Comparison of the ${}^{12}C$ $(e, e^{'} p)$ cross section at low momentum transfer with a relativistic calculation