AltGeoViz enables screen-reader users to interact with dynamic
geovisualizations. Upon loading, users are presented with the title, a summary
of the general spatial pattern, and extrema and average data values (Left). As
users move and zoom, the information is updated, and they can hear the
boundary of their current viewport (Center). Data can be shown at different
geographic units (e.g., state or county level) depending on the zoom level
(Right). See video for a demonstration.

# AltGeoViz: Facilitating Accessible Geovisualization

Chu Li
University of Washington  e-mail<EMAIL_ADDRESS>Rock Yuren Pang
University of Washington  Ather Sharif
University of Washington  Arnavi Chheda-Kothary
University of Washington  Jeffrey Heer
University of Washington  Jon E. Froehlich
University of Washington  e-mail<EMAIL_ADDRESS>
###### Abstract

Geovisualizations are powerful tools for exploratory spatial analysis,
enabling sighted users to discern patterns, trends, and relationships within
geographic data. However, these visual tools have remained largely
inaccessible to screen-reader users. We present AltGeoViz, a new system we
designed to facilitate geovisualization exploration for these users. AltGeoViz
dynamically generates alt-text descriptions based on the user’s current map
view, providing summaries of spatial patterns and descriptive statistics. In a
study of five screen-reader users, we found that AltGeoViz enabled them to
interact with geovisualizations in previously infeasible ways. Participants
demonstrated a clear understanding of data summaries and their location
context, and they could synthesize spatial understandings of their
explorations. Moreover, we identified key areas for improvement, such as the
addition of intuitive spatial navigation controls and comparative analysis
features.

###### keywords:

dynamic geovisualization, accessibility, alt-text, screen-reader

Table 1: Alt-text template and examples of each component.

##  1 Introduction

Geovisualizations are interactive and dynamic visualizations of geographic
information that support exploratory analysis, hypothesis generation, and
communicate information [3, 37]. With improved toolkits [1, 16] and broader
Internet availability, geovisualizations have become key communicative tools
from visualizing COVID occurrences [32] to election results [20]. However,
geovisualizations are inherently visual, making them inaccessible to screen-
reader users unless the visualization creators have explicitly added alt-text
[23, 36]. Even then, the alt-text is static, making it impossible for screen-
reader users to explore and learn from the data interactively. Indeed, a
recent study of 15 geovisualizations by Fan et al. found significant
accessibility issues—none successfully conveyed complex data or higher-level
spatial patterns [8].

While recent work has introduced new data visualization accessibility methods
such as automatic alt-text generation [18, 24, 25], sonification [2, 10, 25],
and haptic graphics [9, 34], this work is primarily aimed at traditional
visualizations (e.g., bar charts, line graphs) rather than geovisualizations.
One exception is Atlas.txt [31], which is a data-to-text natural language
generation system that communicates geo-referenced information through screen-
readers; however, it does not support interactive explorations. Other work in
static map accessibility introduces techniques to verbally query data points
[26], provide enhanced navigational structures [7], and extract data through
sonification [35].

In this paper, we introduce and evaluate new techniques to make interactive
and dynamic geovisualizations accessible to screen-reader users. Our custom
system AltGeoViz auto-generates alt-text based on the user’s viewport,
enabling screen-reader users to navigate, explore, and extract information
from geovisualizations. Specifically, AltGeoViz communicates essential
information to understand geovisualizations including viewport boundaries,
zoom levels, spatial patterns and other summary statistics in any given view.
To evaluate AltGeoViz, we conducted a remote, qualitative user study with five
screen-reader users. Our findings suggest that AltGeoViz enables users to
engage with geovisualizations in ways that were previously infeasible:
participants effectively identified spatial patterns and other statistical
data, and formed spatial understandings of the map based on their
explorations.

In summary, we contribute: (1) AltGeoViz, an open-source system that auto-
generates summaries of interactive and dynamic geovisualizations111GitHub
repository: https://github.com/makeabilitylab/altgeoviz.. (2) Empirical
results from a qualitative evaluation of our system with five screen-reader
users that demonstrates its success in providing accessible geovisualizations
and future enhancement opportunities.

##  2 AltGeoViz Design and Implementation

Drawing on prior strategies for generating alt-text for geovisualizations [31]
and other types of visualizations [13, 15, 23], we describe AltGeoViz’s
design, starting with its spatial pattern summary technique, followed by
providing details on the alt-text generation and prototype implementation. We
present our demo video in the supplementary materials.

###  2.1 Summarizing Spatial Trends

We summarize spatial patterns by dividing any given map view into a $3\times
3$ grid, then spatially grouping regions with similar values. The $3\times 3$
grid paradigm has previously been employed to assist blind and low-vision
users with tasks such as creating graphical information [14] and exploring
maps through sonification [35].

We use a four-step process for grid-based abstraction: (1) Define a bounding
box, which is determined by selecting the smaller of two rectangles: the
bounding box of the geographical dataset (in our example, the 48 contiguous
U.S. states), or the current viewport of the browser. (2) Subdivide the
bounding box into a $3\times 3$ grid, resulting in nine grid cells, Figure 1A.
(3) Assign each polygon in the geographic dataset to the grid cell that
contains the polygon’s centroid, Figure 1B. (4) Aggregate within each grid
cell the data values across all associated polygons, calculating the mean
values, then rank the cells from 1 (highest mean) to 9 (lowest mean), Figure
1C. This process allows us to abstract and translate complex visual trends
into structured, cell-based summaries.

To further simplify the grid summary into natural location descriptors, we
group grid cells based on value similarity and spatial adjacency. This lets
the system generate descriptions with terms like “top-right” instead of cell
numbers. Once the rankings of the grid cells have been established, if four
adjacent cells have sequential rankings (e.g., 1, 2, 3, 4 or 6, 7, 8, 9), we
classify the data value of this group as either high or low, respectively, and
assign the group with a location indicator. For example, if the four cells in
the top-right corner of the $3\times 3$ grid are ranked 1 through 4, we would
report the data pattern as high in the top-right corner of the current map
view. If no set of four adjacent cells meet this criterion, then we check
groupings of three and subsequently two. For these smaller groupings, any
combination of three or two numbers within the sequences 1-2-3-4 or 5-6-7-8
would qualify as a grouping. Figure 2 lists all possible grouping scenarios
and their corresponding location indicators. If no groupings exist, the system
will return: ‘no particular regions with high/low [dataset name]’.

We acknowledge other techniques for summarizing spatial data, such as binning
(e.g. hexbins) [22], kernel density estimation [19], and clustering algorithms
such as K-means [19] or DBSCAN [33]. Most relevant to our work is Atlas.txt
[30, 31], which generates descriptions using improved region growing
segmentation [17].

Figure 1: Grid-based abstraction method for summarizing geovisualization. (A)
The bounding box is subdivided into a 3x3 grid. (B) Each polygon is assigned
to the grid cell containing its centroid. (C) For each cell, the data values
of all associated polygons are aggregated, and the mean value is calculated.
Cells are then ranked from 1 (highest) to 9 (lowest). Figure 2: Possible
scenarios for adjacent cells in sequential ranking and their corresponding
location indicators. Yellow for four, blue for three and green for two
sequentially ranked adjacent cells.

###  2.2 Alt-text Design

Our alt-text design includes the geovisualization description content and
interaction instructions.

Content. Informed by prior work on alt-text content determination for geo-
referenced data [30], and data visualizations more broadly [13, 15, 23], we
design the alt-text template for AltGeoViz to capture essential information of
any given viewport, including the title, boundary, zoom level, spatial
pattern, extremum, and average values. Table 1 presents our complete alt-text
content design and specific examples for each component.

Interaction. Prior work emphasized the importance of initiating alt-text
descriptions with an overview of the visualization and providing detailed
information only upon request [15, 27, 36]. Through iteration and internal
testing, we developed an interaction system that balances immediate feedback
with information load. Upon loading AltGeoViz, the screen-reader announces the
title of the geovisualization, and users can then interact with the map by
pressing the m key. For navigation, the arrow keys assist with panning, and
the +/- keys with zooming in and out. When the navigation keys are pressed,
users receive immediate auditory feedback about the action taken and the new
center of the viewport, such as “Moved right, now centered on Missouri.” For
each view, users can press i to hear the spatial pattern and other data values
or l to hear the locations of the current viewpoint’s four corners. Table 2
lists all shortcut keys and their associated behaviors.

Table 2: List of all shortcut keys and their associated behaviors.

###  2.3 Implementation

AltGeoViz includes a front-end interface implemented in MapboxJS, HTML, CSS,
and JavaScript, and a server that uses the Flask framework in Python. We chose
DuckDB as the database management system for the geospatial data. AltGeoViz
uses Google Cloud for hosting and MongoDB for user log data storage. We
obtained geographic boundaries for 48 contiguous U.S. states and 3,222
counties from TIGER shapefiles [5]. We implemented AltGeoViz using choropleth
(area) maps, future work can extend it to other types, such as symbol maps.

##  3 User Evaluation

To evaluate AltGeoViz, we conducted a remote user study with five screen-
reader users over Zoom. Participants completed a data exploration task with
their chosen screen-reader, after which we asked them questions through a
semi-structured interview. Specifically, our study examined if auto-generating
and auto-updating alt-text for each map view can support users in exploring
and navigating maps effectively (RQ1); extracting the spatial patterns and
other statistics (RQ2); and synthesizing spatial understandings of map
explorations (RQ3). Additionally, we explored participants’ perceptions of
overall system usefulness with both Likert scales [11] and interview questions
(RQ4). Participants received a $30 gift card for one hour of their time.

###  3.1 Participants and Procedure

We recruited five screen-reader users through mailing lists. Prior to the
study, participants filled out a questionnaire to record their demographic
information, screen-reader software, vision-loss level, education level, daily
computer usage, and frequency of interacting with online maps (See
supplementary materials for participant information table). We also provided
participants a link to AltGeoViz’s tutorial site so the participant could test
whether the system’s shortcut keys worked with their device.

Study sessions were conducted over Zoom with one to two researchers per
session. Participants shared their screens when using AltGeoViz and could
pause to ask questions at any time. See supplementary material for a demo of
AltGeoViz.

Introduction and Tutorial. Sessions began with a brief overview of the
project’s motivation and explanation of key concepts related to dynamic
geovisualizations. To build understanding and comfort with AltGeoViz,
participants then used our tutorial website, which featured an interactive
choropleth map that displayed population density across the 48 contiguous U.S.
states. The map included state- and county-level data drawn from the latest
American Community Survey five-year estimates [4]. Once participants felt
familiar with AltGeoViz, the study task commenced.

Study Task. Participants used AltGeoViz to explore a geovisualization similar
to the tutorial but with a new dataset of the percentage of the population
commuting to work by transit. Using AltGeoViz, participants were asked to
answer the following: (1) Which U.S. region has the highest percentage of
transit commuters? (2) Using pan and zoom, which county within that region has
the highest percentage of transit commuters, and what is the percentage value?
(3) Which state has the highest percentage of transit commuters, and how does
this value compare to the county value?

Interview. Sessions concluded with semi-structured interviews and 7-point
Likert scale questions on usability, perceived usefulness, and mental load (7
was the most positive). We also solicited design ideas for future screen-
reader geovisualization systems.

###  3.2 Data and Analysis

All study sessions were audio and video recorded with user consent. Our
analysis focused on summarizing high-level themes through qualitative open
coding [6]. One researcher developed a set of themes based on the video
transcript and observational notes, then thematically coded the responses. A
second researcher verified these themes [28]. The following participant
quotations were slightly modified for concision, grammar, and anonymity.

##  4 Findings

In general, participants responded favorably to AltGeoViz, saying it enabled
new interactions with geovisualizations they had not previously experienced.
Participants could effectively identify spatial patterns and other statistical
data, as well as form spatial understandings of maps based on their
explorations. Nonetheless, participants experienced some challenges in
navigating to specific desired locations. We detail key findings and
suggestions for improving AltGeoViz below.

###  4.1 Feedback on AltGeoViz

Below, we present our findings according to our research questions.

Exploring and navigating maps effectively (RQ1). Four out of five participants
(80%) completed study tasks successfully via panning, zooming, and requesting
viewport boundaries and data summaries. (See supplementary materials for
detailed participants’ performance). Participants remarked on the novelty of
the interactive experience, with P2 saying, “I have never had such an in-depth
interaction with maps before,” and P5 appreciating that “the information would
change depending on your perspective, which is cool.” We observed that
participants enjoyed learning new spatial information and exploring geographic
data distributions, particularly when the information aligned with their prior
knowledge.

The one participant who did not complete the study tasks had difficulty in
navigating to the specific desired location. Participants expressed confusion
when panning the map did not change the county location at the center of their
viewport. As each keystroke pans a fixed number of pixels, navigating across
larger geographic areas often requires multiple keystrokes before centering on
a new region. Most of the participants had not interacted with an interface
similar to AltGeoViz before, but their prior experience with data
visualizations led them to believe that using arrow keys would directly
navigate between discrete geographic regions (P1, P4, P5), rather than
positioning a sliding window to continuously pan across the map. P1 stated
that “It was frustrating not being able to get to where I wanted to fast.” P2
and P3 echoed similar sentiments, with P2 mentioning, “Getting from area to
area [was] a little bit time consuming.” Participants also mentioned that when
they moved outside areas where data was available, they wanted more guidance
on where to navigate next instead of just hearing “Currently out of bounds.
Please move back on the map.” (P2)

Requesting information on location, spatial patterns, and other statistics
(RQ2). Despite some navigational challenges, participants reported high
success in requesting and understanding spatial patterns and data values once
they reached the desired location. All participants felt that it was easy to
request data information (mean=7; SD=0), had a clear understanding of the
spatial summaries and other statistics provided (mean=6.8; SD=0.4), and gave
high ratings for how easy it was to understand their location on the map at
any given time (mean=6.4; SD=0.9). As P3 mentioned, “I like that I can find
information fairly quickly.” P5 appreciated “how intuitive the shortcuts were”
for interactions and noted that “it was really intuitive with which level you
were zoomed in on and what your boundaries were.” P3 echoed this, saying “It
gave me the boundary information, so it was very easy [to know where I was].”
However, P1 warned that location awareness was straightforward given prior
knowledge of U.S. geography, but would be challenging for unfamiliar regions.

Synthesizing spatial understandings from explorations (RQ3).  All participants
could describe the spatial paths they traversed through during the tasks,
regardless of whether they completed the tasks successfully. For example, P1
recalled their navigation process in detail:“From the basic view, I needed to
go to the upper-right-hand corner quickly and efficiently. So I used my big
windows to zoom over, then zoom in. Zoom in to know I am in the upper-right-
hand quadrant.” This illustrates how P1 synthesized the directional movements
and zoom operations into a cohesive mental representation of navigating to the
intended map region.

Perceived utility and mental load (RQ4). All participants felt AltGeoViz was a
posititve step towards making geovisualizations usable and accessible for
screen-reader users. P4 spoke to the prevalence of map visualizations online
but the lack of screen-reader access: “Anytime information needs to be shown,
they’ll put out a map, even for my children’s school. I see them a lot, but
what I don’t see is a useful summary. Even when there is, it’s just a brief
overview that doesn’t answer my specific questions.”

Given such context, participants provided positive feedback and highlighted
how AltGeoViz enabled new interaction experiences with map visualizations. P2
noted, “One of the grad school classes I wanted to take was GIS. But I had to
forego taking that class because there was nothing like this [AltGeoViz ].”
Participants felt AltGeoViz provided meaningful spatial awareness and
perspectives that would have been difficult to achieve through non-interactive
formats. As P1 stated, “I really enjoyed being able to navigate the U.S. and
just get additional data from a graphical perspective,” and “It gives me that
kind of spatial awareness…whereas I would not be able to figure out that with
a drop-down box.”

The introduction of a new interaction technique often comes with increased
cognitive load for users. When asked about the overall mental demand of using
the prototype, participants gave an average rating of 5 out of 7 (SD=1.0).
Participants explained that this level of mental demand stemmed from the
novelty of the interaction itself. As P2 stated, “I’ve never had this in-depth
interaction with maps, so it required quite a bit of cognitive load
initially.”

###  4.2 Suggestions for Improvements

When asked about potential improvements, participants suggested searchability,
comparison capabilities, and complementary information, such as data tables.

Searchability to enhance navigation. To enhance navigation, participants
suggested search functions to let them easily and quickly locate specific
geographic regions on the map. P4 stated, “I’d like to find a way that I could
just get to that specific part of the map quickly.” P3 shared this desire,
stating that “I want a searchable area for my map,” and “I just wish I had a
way of zooming in on a particular [region].” P5 proposed that “Maybe there can
be a little shortcut where you could type in the state abbreviation or the
state name, and then [the system] puts you there.” In addition to search,
participants also mentioned other ways to aid navigation. P1 recommended “some
instant back-to-home button”, and P2 proposed the use of “one letter
navigation.”

Additional information. Participants requested additional information,
including a list of geographical units the view encompassed: “I really liked
the boundaries, but I wanted more information about what was included in those
boundaries or what was outside of those boundaries. Say, there are five states
in your view” (P5). Others suggested an accompanying table available along
with the map, “I’d like a tabular table with the data in; the map’s nice to
navigate around, but I want to just select the state of Kansas instead of
having to arrow all the way around” (P1).

Comparison function. The ability to compare statistics between multiple
geographic areas was a frequently requested feature. P4 stated, “It would be
nice if I could link [Oregon and Washington] together to get statistics.”
Similarly, P2, inspired by the two datasets in the tutorial and the study
task, wanted “a comparative analysis between population density and percentage
of transit commuters” to explore potential correlations between different
datasets.

##  5 Discussion and Conclusion

We presented AltGeoViz, a system that auto-generates and auto-updates
summaries of interactive and dynamic geovisualizations. We found that
AltGeoViz enabled screen-reader users to interact with geovisualizations in
previously infeasible ways. Participants had clear understandings of spatial
patterns, data values and their locations on the map. All participants were
able to verbalize the pathways they took through exploring the data, which
indicates AltGeoViz supported synthesizing spatial understandings.

The study also revealed that participants sometimes struggled with effective
navigation using AltGeoViz, likely due to prior mental models shaped by
linearly navigating web content [29] rather than 2D map exploration.
Participant feedback highlighted the need for more intuitive navigation
capabilities such as text-based search to avoid getting “lost”. Future
iterations should also implement additional user-requested features like
comparison across locations/datasets and accompanying underlying data tables.

A promising future research direction involves developing data-to-text models
capable of summarizing key insights from geovisualizations in more
sophisticated ways, such as employing different classification models, data
aggregation techniques, and clustering algorithms. Such models have the
potential to benefit not just screen-reader users, but also non-screen-reader
users. Prior research has shown that accurately interpreting geovisualizations
like choropleth maps requires some level of geospatial data literacy [12, 21].
Factors like color schemes, area sizing, and data classification methods can
all introduce perceptual biases that hinder people’s ability to accurately
discern meaningful spatial patterns from visualizations [21]. Textual
descriptions that communicate underlying data patterns of geovisualizations
could enhance screen-reader accessibility while serving as an interpretation
aid for a broader audience.

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# Variation of Tensor Force due to Nuclear Medium Effect

Ziming Li1, Jie Zhu1, Taofeng Wang1∗, Minliang Liu2, Jiansong Wang2,
Yanyun Yang2, Chengjian Lin3, Zhiyu Sun2, Qinghua He4, M. Assié5,Y. Ayyad6,
D. Beaumel5, Zhen Bai2, Fangfang Duan2, Zhihao Gao2, Song Guo2, Yue Hu1,
Wei Jiang7, F. Kobayashi8, Chengui Lu2, Junbing Ma2, Peng Ma2,
P. Napolitani9, G. Verde10,11, Jianguo Wang2, Xianglun Wei2, Guoqing Xiao2,
Hushan Xu2, Biao Yang7, Runhe Yang2, Yongjin Yao1, Chaoyue Yu2,
Junwei Zhang2, Xing Zhang2, Yuhu Zhang2, Xiaohong Zhou2 1School of Physics,
Beihang University, Beijing 100191, China
2Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China
3China Institute of Atomic Energy, P.O. Box 275 (10), Beijing 102413, China
4Department of Nuclear Science $\&$ Engineering, College of Material Science
and Technology,
Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
5IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405 Orsay, France
6Facility for Rare Isotope Beams, Michigan State University, East Lansing,
Michigan 48824, USA
7State Key Laboratory of Nuclear Physics and Technology, School of Physics,
Peking University, Beijing 100871, China
8Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama,
Toyonaka, Osaka 560-8531, Japan
9IPN, CNRS/IN2P3, Université Paris-Sud 11, Université Paris-Saclay, 91406
Orsay Cedex, France
10INFN Sezione di Catania, via Santa Sofia 64, I-95123 Catania, Italy
11Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), Université de Toulouse,
CNRS, UPS, F-31062 Toulouse Cedex 9, France

###### Abstract

The enhancement of $J^{\pi}(T)$=3+(0) state with isospin $T=0$ excited by the
tensor force in the free 6Li nucleus has been observed, for the first time,
relative to a shrinkable excitation in the 6Li cluster component inside its
host nucleus. Comparatively, the excitation of $J^{\pi}(T)$=0+(1) state with
isospin $T=1$ for these two 6Li formations take on an approximately equal
excitation strength. The mechanism of such tensor force effect was proposed
due to the intensive nuclear medium role on isospin $T$=0 state.

###### pacs:

Valid PACS appear here

††preprint: APS/123-QED

Tensor force has been proved to be of importance in reproducing the properties
of nuclear matter and explaining the D-wave mixing and binding energy in
deuterons. Some studies have shown that the tensor force may play a
significant role in the properties of the new magic number of neutron rich
nuclei and the order changes of single particle orbits. Tensor force
essentially make variations in single-particle energy causing the shell
evolution [1]. Tensor force also contributes to the reduction of the spin-
orbits splitting [2, 3] and to the attractive role in the nuclear binding
energy [4].

The studies of the short-range correlation indicate that the high momentum
component in the wave functions of the nucleon momentum distribution larger
than the Fermi momentum mainly comes from the tensor force inductions of
proton-neutron correlated pairs [5, 6]. The spins of neutron and proton
($\bm{s_{n}}$, $\bm{s_{p}}$) can be either parallel ($I$=1; $l$=0, 1, 2) or
antiparallel ($I$=0; $l$=1), where $\bm{I=s_{n}+s_{p}}$ and $\bm{J=I+l}$.
There are four ways to couple $\bm{s_{n}}$, $\bm{s_{p}}$ and $\bm{l}$ to get a
measured total $J$ = 1 for deuteron. The parity of deuteron is associated with
the orbital motion of (-1)l. The observed even parity for deuteron leads to
eliminate the combination of spins that include $l$=1, leaving $l$=0 and $l$=2
as possibilities. The wave function of the deuteron is therefore consist of
the mixture of S and D components.

The spin and isospin of nucleons in proton-neutron ($pn$) pair can be combined
into different channels. Tensor force has a strong population strength for the
spin and isospin for $J,T$ = 1, 0 channel, but a weak one for $J,T$ = 0, 1
channel [7]. The proton-neutron tensor monopole interaction ($T$ = 0) is twice
as strong as the $T$ = 1 interaction [8]. For the same radial condition of
wave function, larger orbital angular momentums of proton and neutron subshell
may intensively enhance the tensor monopole effect when their relative
momentum becomes higher [1, 8].

The interaction properties of the tensor force component depend on the
orientation direction of spins of proton and neutron relative to the direction
of the vector connecting them [9]. The tensor force conducts between two
nucleons with their spins aligned, and the interaction is attractive when the
spins are parallel to the line connecting the two nucleons and repulsive when
the spins are perpendicular to this line [9].

The configuration of the two-body cluster in 6Li can be represented by p-shell
nucleons of $pn$ pair (deuteron) coupled to s-shell nucleons of the $\alpha$
core with intrinsic spin 1 and intrinsic orbital angular momentum $l$ = 0 as
well as relative momentum $L$ = 0, generating the 1+ ground state and the
excited triplet states 1+, 2+, 3+ with isospin $T$ = 0 of 6Li from $L$ = 2
[10]. The cluster-cluster spin-orbit force splits the $L$ = 2 as these triplet
states, where $L$ the orbital momentum coupling of $pn$ pair and $\alpha$. The
small magnitude with a negative sign for the electric quadrupole moment of 6Li
was suggested to be accounted for by introducing the cluster-cluster tensor
interaction which mixes a small $L$ = 2 component into the 6Li states [10].

11C is a proton-rich isotope with six protons and five neutrons. This
asymmetry in the proton-to-neutron ratio can significantly affect the
stability and behavior of the nucleus. The strong Coulomb repulsion between
protons makes this nuclei prone to form the cluster structure with the general
formalism of $\alpha$ and the tensor force favored $pn$ pair of $d$.
$d$+$\alpha$ are feasible to form the weakly bound 6Li nuclei within 11C.

In this letter, we present an inspired aspect of tensor force effect
enhancement drived by isospin $T$ = 0 state with large spin $J^{\pi}$ = 3+ in
the free 6Li, while a shringking effect evidently in the 6Li cluster inside
nucleus due to the nuclear medium. Comparatively, the isospin $T$=1 with
$J^{\pi}$ = 0+ state maintains an equal excitation strength in these two
different 6Li formations.

The present experimental measurement was performed at the Radioactive Ion Beam
Line at the Heavy Ion Research Facility in Lanzhou (HIRFL-RIBLL) [11]. A 60
MeV/nucleon 12C beam was transfed to bombard a 3.5 mm 9Be target to produce
about 25 MeV/nucleon 11C secondary beam with a purity of about 99$\%$ and an
intensity of about 104 particles per second. The beam particles were
identified in terms of $B\rho-$TOF$-\Delta E$ method with the magnets and two
plastic scintillator detectors in the beam line [26]. The 11C secondary beam
were bombarded on a 50 mg/cm2 carbon target to produce the breakup reaction.

Three parallel plate avalanche chambers (PPACs) with 50$\times$50 mm2 active
area and position resolutions of about 1 mm (FWHM) in both the $X$ and $Y$
directions were placed in front of the target to track the incident 11C beam
[12] and to subsequently get the reaction vertex in the target. $d$ and
$\alpha$ are detected by the zero-degree telescope system which consists of a
double-sided silicon strip detector (DSSD, of 148 $\mu$m in thickness and
50$\times$50 mm2 in cross-sectional area) with 32 strips on both front and
back sides, and a 2$\times$2 photodiode (PD) readout CsI (Tl) scintillator
(25$\times$25$\times$30 mm3 size for each unit) array. Each CsI (Tl)
scintillator is covered by two layers of high reflection Tyvek papers and a 10
$\mu$m aluminum coated Mylar film as window. The PD is coupled to CsI (Tl)
scintillator with the photoconductive silicone grease. The angular coverage of
the zero-degree telescope is about 0-9∘. Five LaBr3 (Ce) and one NaI
scintillator detectors were placed around the target to measure the decayed
$\gamma$s from the excited fragments. DSSD was utilized to record the
$\Delta$E energy and the position of the detecting fragments, therefore, the
emission angle may be obtained by combining with the reaction vertex in the
target. CsI (Tl) detection system provides the residual E energy of the
fragments. Particle identifications (PID) for $\alpha$ and $d$ were performed
using $\Delta$E-E contour. The energy resolution with sigma of this
$\Delta$E-E detection system is estimated to be $\sim$0.8 MeV from numerical
simulation.

Figure 1:  Excitation energy spectra of 6Li∗: (a) Under the cut of
$\Theta_{CM}<120^{\circ}$ where $\Theta_{CM}$ is the relative emitting angle
between $d$ and $\alpha$ in the center-of-mass-system of 6Li, clear excited
states of $J^{\pi}(T)=3^{+}(0)$ and $J^{\pi}(T)=0^{+}(1)$ are observed; (b)
Under the cut of $\Theta_{CM}>120^{\circ}$ there exhibits a enhanced
population of $J^{\pi}(T)=3^{+}(0)$ state, while $J^{\pi}(T)=0^{+}(1)$ state
keeps a similar population to that in (a). The purple dash lines are the
fitting for these resonances with Breit-Wigner function, the continuous
background is assigned by the green line. Figure 2:  The relative emitting
angle $\Theta_{CM}$ between $d$ and $\alpha$ in the center-of-mass-system of
6Li. There exist two regions separated by $120^{\circ}$. The smaller
$\Theta_{CM}$ region corresponds to $d$ and $\alpha$ emitted by the 6Li
cluster component initially inside 11C, comparatively, the larger
$\Theta_{CM}$ reflects the back-to-back emission of $d$ and $\alpha$ from the
flying 6Li isolated from 11C.

The excited state of 6Li∗ was reconstructed by the invariant mass of final
state particles of $d$ and $\alpha$ selected with the multiplicity-2 hits
events recorded by the zero-degree telescope system. The excitation energy
spectra of 6Li∗ are investigated with two cases (Fig. 1) in terms of the
relative emitting angle $\Theta_{CM}$ between $d$ and $\alpha$ in the center-
of-mass-system of 6Li: (a) $\Theta_{CM}<120^{\circ}$; (b)
$\Theta_{CM}>120^{\circ}$.

Under the case of $\Theta_{CM}<120^{\circ}$, the resonance states of
$J^{\pi}(T)=0^{+}(1)$ and $3^{+}(0)$ can be clearly observed, and their
magnitude are comparable (Fig. 1 (a)). Contrastingly, the cross section of
$J^{\pi}(T)=3^{+}(0)$ under the case of $\Theta_{CM}>120^{\circ}$ (Fig. 1 (b))
extremely enhances relative to that under the case of
$\Theta_{CM}<120^{\circ}$ (Fig. 1 (a)). While the magnitude of the cross
sections of $J^{\pi}(T)=0^{+}(1)$ state are similar between these two cases.
The small relative angle $\Theta_{CM}<120^{\circ}$ indicates $d$ and $\alpha$
arise from 11C direct breakup process, since their momenta should be balanced
by other fragments. In the case of $\Theta_{CM}>120^{\circ}$, the large
relative emission angle implies that $d$ and $\alpha$ are emitted by back-to-
back emission mode and $d$ and $\alpha$ are decay products from the flying 6Li
nucleus isolated from 11C. The flying isolated 6Li∗ was confirmed by the clear
asymmetry edge of the decay $\gamma$ spectrum of 6Li∗ due to the Doppler-shift
effect.

The cross section ratio between $J^{\pi}(T)=3^{+}(0)$ state and
$J^{\pi}(T)=0^{+}(1)$ state varies from 2.7 at $\Theta_{CM}<120^{\circ}$ to
5.5 at $\Theta_{CM}>120^{\circ}$, implying a remarkable property: the isospin
$T$=0 state of $J^{\pi}=3^{+}$ in the isolated 6Li is extremely strengthened,
however, this state is hindered extremely in the 6Li cluster component inside
11C. Comparatively, the isospin $T$=1 state of $J^{\pi}=0^{+}$ keeps an almost
equal excitation under these two different 6Li formations.

The transverse momentum $p_{T}$ of $d$ or $\alpha$ fragments reflects the
dynamical essentiallities of clusters in the initial state in the 6Li. $p_{T}$
is also equal to the transfer momentum $\Delta p$ in the 6Li breakup reaction,
and therefore,

$\begin{split}sin\Theta_{CM}=\frac{\Delta p}{p}=\frac{F\Delta
t}{p}\simeq\frac{1}{p}\frac{V_{0}}{R}\frac{R}{v}=\frac{V_{0}}{pv}=\frac{V_{0}}{2E_{k}},\end{split}$
(1)

where $p$ is the momentum of the $d$ or $\alpha$ fragment. $F$ the average
force between $d$ and $\alpha$ is proportional to $\frac{V_{0}}{R}$, where
$V_{0}$ and $R$ are the depth and range of potential between $d$ and $\alpha$.
Assume the velocity of the $d$ or $\alpha$ cluster is $v$, the lifetime of the
6Li excited state can be expressed as $\tau$ = $\Delta t=\frac{R}{v}$. $E_{k}$
is the kinematic energy of $d$ or $\alpha$. According to Equ. (1), the
$J^{\pi}(T)$=$3^{+}(0)$ excited state with the open angle of $d$ and $\alpha$
of $\Theta_{CM}<120^{\circ}$ corresponding to 6Li inside 11C have a longer
lifetime than that of $\Theta_{CM}>120^{\circ}$ corresponding to the isolate
6Li. It is also reasonable to deduce that $d$ or $\alpha$ acts a slower
dynamics with a smaller $E_{k}$ in the 6Li component in the nuclear medium
relative to in the isolate 6Li.

Figure 3:  The relative momentum $p_{rel}$ between $d$ and $\alpha$ dependent
on the spin of the triplet state with $T$=0. $J^{\pi}(T)$=3${}^{+}(0)$ state
lies in the lower $p_{rel}$ region with a wider width,
$J^{\pi}(T)$=2${}^{+}(0),1^{+}(0)$ mixing states locate in the higher
$p_{rel}$ region with a narrower width.

Nucleons correlation and clustering are the universal characteristic in
nuclei, especially the existing molecular-like states in the neutron-rich
light nuclei. The cluster indicates a spatially localized subsystem consisted
of strongly correlated nucleons, such as Deutron-like short range correlated
pair and the compact four-nucleon correlated $\alpha$ cluster. The relative
motion between clusters become as a remarkable quantity for the fundamental
motion mode of the nucleus.

The cluster model is treated based on a different degree of freedom than on
the other models, typically the one-center mean field shell model. The
microscopic cluster keep a dynamical process in that the everlasting change
structure due to its formation, growth and breakup complemented with the
shell-model-like states simultaneously. It is a significant fact that the
description for such transition of structure is identified in a finite quantum
many-body system of the atomic nucleus. The inter-cluster relative motion and
its coupling with the excitation modes of clusters correspond to not only the
bound-state but also to the highly excited states like molecular resonances.

As shown in Fig. 3, the distribution of relative momentum
$\vec{p}_{rel}=\vec{p}_{\alpha}-\vec{p}_{d}$ between $d$ and $\alpha$ in the
center-of-mass system of 6Li at $3^{+}(0)$ state lies in the low $p_{rel}$
region, while $2^{+}(0)$ and $1^{+}(0)$ mixing states locate at high $p_{rel}$
region. With Gaussian fitting, the mean value of $3^{+}(0)$ state was given to
be 361.6 $\pm$ 12.7 MeV/c, and the standard deviation $\sigma$ is 77.2 $\pm$
5.5 MeV/c. And the mean value of the mixing state of $2^{+}(0)$ and $1^{+}(0)$
is 517.7 $\pm$ 9.1 MeV/c, and $\sigma$ of 35.5 $\pm$ 2.8 MeV/c. It indicates
that the low relative momentum for $d$ and $\alpha$ with a large width of
momentum distribution in $3^{+}(0)$ state correspond to a weak relatively
dynamical motion with a narrow pn pair spatial distribution; the higher
relative momentum with a smaller width for $2^{+}(0)$ and $1^{+}(0)$ mixing
states maintain a drastic relative motion and a broad occupation for the pn
pair + $\alpha$ cluster in 6Li.

The tensor force strength for $J^{\pi}(T)=0^{+}(1)$ state is much smaller than
that for $J^{\pi}(T)=3^{+}(0)$ state in the isolated 6Li [13], which can be
essentially explained by the tensor force properties of the isospin dependence
[7]. For the $0^{+}(1)$ state, which has a configuration of
$(0s_{1/2})^{4}(0p_{3/2})^{2}$, the inner 4He core composed of two $pn$ pairs
with $T$=0 is excited from 0$s$ to 0$p_{1/2}$ by the tensor force via two-
particle two-hole (2p2h) mode, while the outer $pn$ pair on the 0$p$ shell
with $T$=1 takes a relatively small excitation due to the weak tensor force
for the $T$=1 channel. For the $3^{+}(0)$ state, the outer $pn$ pair in the
0$p$ shell may take place a tensor force excitation with a $T$=0 state from
$(0p_{3/2})^{2}$ to $(0d_{3/2})^{2}$, which satisfy the selection rule for the
tensor force excitation of $\Delta L$=2, $\Delta S$=2 and $\Delta J$=0. From
the point view of excitation strength of tensor force, the coupling of outer
$pn$ pair to the inner 4He core is relatively weak for $=0^{+}(1)$ state and
hence the population of $3^{+}(0)$ state is much higher than that of
$0^{+}(1)$ state in the isolated 6Li nucleus, as shown in Fig. 2(b).

However, when 6Li is not completely isolated but still within the domain of
11C as a component, $d$ and $\alpha$ in 6Li are correlated two-body clusters
and essentially affected by the central interactions from the residual
nucleus. Such extra interactions may reduce the strength of coupling of the
$pn$ pair with isospin $T$ = 0 to $\alpha$, which leads to the shrinkage of
tensor force excitation and results in a comparable populations between
$J^{\pi}(T)=0^{+}(1)$ state and $J^{\pi}(T)=3^{+}(0)$ state for the case of
$\Theta_{CM}<120^{\circ}$, as shown in Fig. 1(a).

Among the $T$=0 triplet states of $J^{\pi}(T)=3^{+}(0),2^{+}(0),1^{+}(0)$, the
strong excitation of $3^{+}(0)$ state with the lowest excitation energy
results from tensor force excitation from $(0p_{3/2})^{2}$ to $(0d_{3/2})^{2}$
with 2p2h excitation mode at a high spin and $T$=0. The highest excited energy
state $1^{+}(0)$ involves the mixing configurations of
$(0s_{1/2})^{4}(0p_{3/2})^{2}$, $(0s_{1/2})^{4}(0p_{1/2})^{1}(0p_{3/2})^{1}$
and $(0s_{1/2})^{4}(0p_{1/2})^{2}$ with a similar probability each other, and
$2^{+}(0)$ state only takes on a configuration of
$(0s_{1/2})^{4}(0p_{1/2})^{1}(0p_{3/2})^{1}$ with two valence nucleons of
neutron and proton lying in the separated sub-shell levels [13], which could
explain the present experimental observations of the high population of
$3^{+}(0)$ state and the low population of $2^{+}(0)$ and $1^{+}(0)$ states.
In addition, This could also clarify the relatively large dynamical motion and
broader density distribution of $d$ and $\alpha$, namely, a more loosely bound
structure for $2^{+}(0)$ and $1^{+}(0)$ states in 6Li.

The lightest even neutron rich nucleus is considered to be the best nuclear
molecule object. The valence neutrons may occupy the $\sigma$\- or $\pi$\-
valence orbits around the separated $\alpha$ clusters. The $\pi$\- valence
neutrons move in a circular orbit centered on the deformation axis, while the
density of the motion orbit of the $\sigma$\- valence neutrons increases along
the axis between the $\alpha$s. Because of Pauli’s principle, the neutrons in
the $\sigma$ orbit tend to push the $\alpha$ cluster far away, which leads to
the more deformed structure. As concerned to 6Li, it is the lightest one-
centered $\alpha$ cluster with a valence pn pair, the $\alpha$ core
repulsively deviates away from the the $\sigma$-orbital valence neutron. The
formation of 6Li is really an oblate shape which is reflected by the very
small magnitude with a negative sign for electric quadrupole moment of 6Li
[14-16].

Figure 4:  The tensor force strength ratio of without the nuclear medium to
within the nuclear medium $f/f_{0}$ depending on the atomic number A, where
NEMT model calculations are performed with two functions of nuclear density
$\rho_{ch}$ and $\rho_{ws}$.

The tensor force strength, modulated by the nuclear medium effects, reflects
the intricate interplay between the nucleons within the nucleus. As the
nuclear density increases, more nucleons are packed into a given volume,
leading to increased overlap and interaction between them. This enhanced
interaction modifies the strength of the tensor force and its impact on the
nuclear system.

$\begin{split}\frac{f(\rho)}{f_{0}(\rho)}=e^{-(a\rho+b\rho^{2}+c\rho^{3})}\end{split}$
(2)

The function $f(\rho)/f_{0}(\rho)$ of nuclear medium effect for tensor force
strength (NMET) in Equ. (2) captures this behavior by introducing the scaling
constant $a,b,c$. The positive values of which indicate that the tensor force
strength diminishes as the nuclear density increases. This decrease is a
manifestation of the saturation of the strong nuclear force at high densities,
where the repulsive interactions between nucleons begin to dominate,
counteracting the attractive tensor force. The density distributions of the
nucleus which are usually described by a Woods-Saxon type distribution as

$\begin{split}\rho_{ws}(r)=\rho_{0}\left[1+exp\left(\frac{r-R}{a}\right)\right]^{-1}\end{split}$
(3)

with diffuseness parameter $a\sim$ 0.53 fm and $\rho_{0}\sim$ 0.17 fm-1 is the
density at the center of the nucleus. The radius parameter $R$ is formed by
mass number $A$ as $R\sim 1.10A^{1/3}$ (fm). A charge density function was
approximated as Equ. (4), which treats the shape of the nuclei as a uniform
sphere with a constant charge density [17].

$\begin{split}\rho_{ch}(r)=\frac{0.75A/\pi}{(5/3<r^{2}>)^{3/2}}\end{split}$
(4)

The calculations of with and without $b$, $c$ terms in Equ. (2) defining as
NMET-1 and NMET-2 models have been performed with two nuclear density
functions of Equ. (3) and Equ. (4), as shown in Fig. 4. The parameters were
ajusted according to the scaling of tensor force with nuclear density to
consistent to the present experimental data of 3+(0) state of 6Li. A
saturation trend is achieved at high densities, reflecting the intricate
behavior of the strong nuclear force within atomic nuclei.

The modification of tensor force strength with nuclear density effects becomes
particularly important in extreme conditions, such as neutron stars or during
heavy-ion collisions in nuclear physics experiments. In these extreme
environments, the nuclear density can reach values far beyond those found in
stable atomic nuclei. The modification of the tensor force strength with
nuclear density effects influences the equation of state, nuclear structure,
and transport properties of nuclear matter.

Summarily, a shrink excitation for spin $J^{\pi}=3^{+}$ state with isospin
$T=0$ was observed in the 6Li cluster component inside the nucleus for the
first time, which distinctly differs from the relatively enhanced excitation
of this state in the isolated nucleus 6Li. While the excitation of the
reference state of $J^{\pi}=0^{+}$ with isospin $T=1$ exhibits an almost equal
cross section for these two 6Li formations. The mechanism of this relatively
weaker excitation in the 6Li cluster in 11C nucleus is proposed due to the
nuclear medium effects hindering the tensor force excitation for the isospin
$T$ = 0 state, but no impact on the $T=1$ state.

We would like to acknowledge the staff of HIRFL for the operation of the
cyclotron. The author T. Wang appreciates for the financial supports from
China Scholarship Council. This work has also been supported by the National
Natural Science Foundation of China (No. 10175091 and No. 11305007).

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