Improved structure of calcium isotopes from <i>ab initio</i> calculations
M. Heinz, T. Miyagi, S. R. Stroberg, A. Tichai, K. Hebeler, A. Schwenk
Abstract
The in-medium similarity renormalization group (IMSRG) is a powerful and flexible many-body method to compute the structure of nuclei starting from nuclear forces. Recent developments have extended the IMSRG from its standard truncation at the normal-ordered two-body level, the IMSRG(2), to a precision approximation including normal-ordered three-body operators, the IMSRG(3)- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msup> <a:mi>N</a:mi> <a:mn>7</a:mn> </a:msup> </a:math> . This improvement provides a more precise solution to the many-body problem and makes it possible to quantify many-body uncertainties in IMSRG calculations. We explore the structure of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mmultiscripts> <b:mi>Ca</b:mi> <b:mprescripts/> <b:none/> <b:mrow> <b:mn>44</b:mn> <b:mo>,</b:mo> <b:mn>48</b:mn> <b:mo>,</b:mo> <b:mn>52</b:mn> </b:mrow> </b:mmultiscripts> </b:math> using the IMSRG(3)- <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msup> <c:mi>N</c:mi> <c:mn>7</c:mn> </c:msup> </c:math> , focusing on understanding existing discrepancies of the IMSRG(2) to experimental results. We find a significantly better description of the first <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msup> <d:mn>2</d:mn> <d:mo>+</d:mo> </d:msup> </d:math> excitation energy of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mmultiscripts> <e:mi>Ca</e:mi> <e:mprescripts/> <e:none/> <e:mn>48</e:mn> </e:mmultiscripts> </e:math> , improving the description of the shell closure at <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>N</f:mi> <f:mo>=</f:mo> <f:mn>28</f:mn> </f:mrow> </f:math> . At the same time, we find that the IMSRG(3)- <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msup> <g:mi>N</g:mi> <g:mn>7</g:mn> </g:msup> </g:math> corrections to charge radii do not resolve the systematic underprediction of the puzzling large charge radius difference between <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mmultiscripts> <h:mi>Ca</h:mi> <h:mprescripts/> <h:none/> <h:mn>52</h:mn> </h:mmultiscripts> </h:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mmultiscripts> <i:mi>Ca</i:mi> <i:mprescripts/> <i:none/> <i:mn>48</i:mn> </i:mmultiscripts> </i:math> . We present estimates of many-body uncertainties of IMSRG(2) calculations applicable also to other systems based on the size extensivity of the method.