The Three-Boson System at Next-to-Next-to-Leading Order
We discuss effective field-theory treatments of the problem of three particles interacting via short-range forces (range R
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| Veröffentlicht in: | Few-body systems 2006-12, Vol.40 (1-2), p.35-55 |
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| container_title | Few-body systems |
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| creator | Platter, L. Phillips, D. R. |
| description | We discuss effective field-theory treatments of the problem of three particles interacting via short-range forces (range R |
| doi_str_mv | 10.1007/s00601-006-0165-z |
| format | Article |
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R.</creator><creatorcontrib>Platter, L. ; Phillips, D. R.</creatorcontrib><description>We discuss effective field-theory treatments of the problem of three particles interacting via short-range forces (range R << a 2, with a 2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude whose low-momentum part is renormalization-group invariant up to corrections of O(R 3/a 2 3). Since corrections of O(R/a 2) and O(R 2/a 2 2) can be straightforwardly included in the integral equation's kernel, a unique solution for 1 + 2 scattering phase shifts and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement with recent three-dimensional Faddeev calculations that used phenomenological inter-atomic potentials. 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R.</creatorcontrib><title>The Three-Boson System at Next-to-Next-to-Leading Order</title><title>Few-body systems</title><description>We discuss effective field-theory treatments of the problem of three particles interacting via short-range forces (range R << a 2, with a 2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude whose low-momentum part is renormalization-group invariant up to corrections of O(R 3/a 2 3). Since corrections of O(R/a 2) and O(R 2/a 2 2) can be straightforwardly included in the integral equation's kernel, a unique solution for 1 + 2 scattering phase shifts and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement with recent three-dimensional Faddeev calculations that used phenomenological inter-atomic potentials. [PUBLICATION ABSTRACT]</description><subject>Correlation</subject><subject>Helium</subject><subject>Integrals</subject><subject>Invariants</subject><subject>Kernels</subject><subject>Linear equations</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Scattering</subject><subject>Scattering amplitude</subject><subject>Theory</subject><subject>Three dimensional</subject><subject>Trimers</subject><issn>0177-7963</issn><issn>1432-5411</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNpdkE1PAjEURRujiYj-AHcTV26q7_VzulQiakJkIa6bTtsRCMxgOyTCr3cIunFz7-Kd3LwcQq4R7hBA32cABUj7pIBK0v0JGaDgjEqBeEoGgFpTbRQ_Jxc5LwFQGoQB0bN5LGbzFCN9bHPbFO-73MV14briLX53tGvpX0-iC4vms5imENMlOavdKser3x6Sj_HTbPRCJ9Pn19HDhHoOsqPaS8mxLKXzAbzBKggnaleLCsqqDoyBlKpyuj8zzmKsEUxwonRM6OBLzYfk9ri7Se3XNubOrhfZx9XKNbHdZotKa2OYUaxHb_6hy3abmv47y0BxNKU-QHiEfGpzTrG2m7RYu7SzCPZg0h5N2j7twaTd8x_AimTj</recordid><startdate>20061201</startdate><enddate>20061201</enddate><creator>Platter, L.</creator><creator>Phillips, D. 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R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Three-Boson System at Next-to-Next-to-Leading Order</atitle><jtitle>Few-body systems</jtitle><date>2006-12-01</date><risdate>2006</risdate><volume>40</volume><issue>1-2</issue><spage>35</spage><epage>55</epage><pages>35-55</pages><issn>0177-7963</issn><eissn>1432-5411</eissn><coden>FBSYEQ</coden><abstract>We discuss effective field-theory treatments of the problem of three particles interacting via short-range forces (range R << a 2, with a 2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude whose low-momentum part is renormalization-group invariant up to corrections of O(R 3/a 2 3). Since corrections of O(R/a 2) and O(R 2/a 2 2) can be straightforwardly included in the integral equation's kernel, a unique solution for 1 + 2 scattering phase shifts and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement with recent three-dimensional Faddeev calculations that used phenomenological inter-atomic potentials. [PUBLICATION ABSTRACT]</abstract><cop>Wien</cop><pub>Springer Nature B.V</pub><doi>10.1007/s00601-006-0165-z</doi><tpages>21</tpages></addata></record> |
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| identifier | ISSN: 0177-7963 |
| ispartof | Few-body systems, 2006-12, Vol.40 (1-2), p.35-55 |
| issn | 0177-7963 1432-5411 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Correlation Helium Integrals Invariants Kernels Linear equations Mathematical analysis Mathematics Scattering Scattering amplitude Theory Three dimensional Trimers |
| title | The Three-Boson System at Next-to-Next-to-Leading Order |
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